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Abstract: Labelle and Lamathe introduced in 2009 a generalization of the standard combinatorial differential species operator D, by giving a combinatorial interpretation to , where and are two-sort and one-sort species respectively. One can show that such operators can be decomposed as sums of products of simpler operators called atomic combinatorial differential operators. In their paper, Labelle and Lamathe presented a list of the first atomic differential operators. In this paper, we describe an algorithm that allows to generate (and enumerate) all of them, subject to available computer resources. We also give a detailed analysis of how to compute the molecular components of . [Copyright &y& Elsevier]

Abstract: This paper proposes a four dimensional orthogonal packing and time scheduling problem. The problem differs from the classical packing problems in that the position and orientation of each item in the container can be changed over time. In this way, the four dimensional space–time problem better uses the container time. Also, we consider a general case that all parameters are real numbers, which makes the problems more difficult to solve. This paper proposes an algorithm and proves that the algorithm could solve the problem optimally by a finite number of operations. We say this problem is weak computational, meaning that if there exists a universal machine that could represent real numbers and could do unit arithmetic or logical operation on real numbers in finite time, then the algorithm could find optimal solutions in finite time. This paper also presents a proof of the weak computability over a general case of the three dimensional orthogonal packing problem where all parameters are positive real numbers. [Copyright &y& Elsevier]

Abstract: This paper describes the biological and theoretical foundations of a new Artificial Immune System the Receptor Density Algorithm. The algorithm is developed with inspiration from T cell signalling processes and has application in anomaly detection. Connections between the Receptor Density Algorithm and kernel density estimation with exponential smoothing are demonstrated. Finally, the paper evaluates the algorithm’s performance on two types of anomaly detection problem. [Copyright &y& Elsevier]

Abstract: This paper extends a result of Graillat, which was based on Rump’s Theorem, to show that pseudospectra of matrix polynomials expressed in other bases, and also some nonlinear matrix functions, are unaffected by drawing the matrix coefficients from certain structured families. We show by example that this behaviour is not universal. This result is of interest because computation of structured pseudospectra is much more expensive in general than computation of unstructured pseudospectra, and in the cases covered by Rump’s Theorem there is no point going to the extra effort. The paper also contains some examples that may be of interest to the community, including an analytical solution of a nested exponential equation that shows why exponential polynomial decomposition algorithms may be of interest. [Copyright &y& Elsevier]

Abstract: In this paper, we study the geodetic convexity of graphs, focusing on the problem of the complexity of computing a minimum hull set of a graph in several graph classes. For any two vertices of a connected graph , the closed interval of and is the set of vertices that belong to some shortest -path. For any , let . A subset is geodesically convex or convex if . In other words, a subset is convex if, for any and for any shortest -path , . Given a subset , the convex hull of is the smallest convex set that contains . We say that is a hull set of if . The size of a minimum hull set of is the hull number of , denoted by . The Hull Number problem is to decide whether , for a given graph and an integer . Dourado et al. showed that this problem is NP-complete in general graphs. In this paper, we answer an open question of Dourado et al. (2009) [1] by showing that the Hull Number problem is NP-hard even when restricted to the class of bipartite graphs. Then, we design polynomial-time algorithms to solve the Hull Number problem in several graph classes. First, we deal with the class of complements of bipartite graphs. Then, we generalize some results in Araujo et al. (2011) [2] to the class of -graphs and to cacti. Finally, we prove tight upper bounds on the hull numbers. In particular, we show that the hull number of an -node graph without simplicial vertices is at most in general, at most if is regular or has no triangle, and at most if has girth at least . [Copyright &y& Elsevier]

Abstract: Reaction systems are a formal model based on the regulation mechanisms of facilitation and inhibition between biochemical reactions, which underlie the functioning of living cells. The aim of this paper is to explore the expressive power of reaction systems as a modeling framework, showing how their basic assumptions and properties can be exploited to formalize computer science and biology oriented problems. In this view, we first provide a reaction-based description of an iterative algorithm to solve the Tower of Hanoi puzzle. Then, we show how the regulation of gene expression in the lac operon, involved in the metabolism of lactose in Escherichia coli cells, can be formalized in terms of reaction systems. Finally, we present a method to derive, given a reaction system with reactions, a functionally equivalent system with reactions using simplification methods of boolean expressions. Some final remarks and directions for future research conclude the paper. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the model of communication where wireless devices can either switch their radios off to save energy (and hence, can neither send nor receive messages), or switch their radios on and engage in communication. The problem has been extensively studied in practice, in the setting such as deployment and clock synchronization of wireless sensor networks. We distill a clean theoretical formulation of minimizing radio use and present near-optimal solutions. Our base model ignores issues of communication interference, although we also extend the model to handle this requirement. We assume that nodes intend to communicate periodically, or according to some time-based schedule. Clearly, perfectly synchronized devices could switch their radios on for exactly the minimum periods required by their joint schedules. The main challenge in the deployment of wireless networks is to synchronize the devices’ schedules, given that their initial schedules may be offset relative to one another (even if their clocks run at the same speed). In this paper, we study how frequently the devices must switch on their radios in order to both synchronize their clocks and communicate. In this setting, we significantly improve previous results, and show optimal use of the radio for two processors and near-optimal use of the radio for synchronization of an arbitrary number of processors. In particular, for two processors we prove deterministic matching upper and lower bounds on the number of times the radio has to be on, where is the discretized uncertainty period of the clock shift between the two processors. (In contrast, all previous results for two processors are randomized.) For processors (for any positive ) we prove is the lower bound on the number of times the radio has to be switched on (per processor), and show a nearly matching (in terms of the radio use) Õ randomized upper bound per processor. For our algorithm runs with at most poly-log radio invocations per processor. Our bounds also hold in a radio-broadcast model where interference must be taken into account. [Copyright &y& Elsevier]

Abstract: On-line algorithms have been extensively studied for the one-dimensional bin packing problem. In this paper, we investigate two classes of one-dimensional bin packing algorithms, and we give better lower bounds for their asymptotic worst-case behavior. For on-line algorithms so far the best lower bound was given by van Vliet in (1992) . He proved that there is no on-line bin packing algorithm with better asymptotic performance ratio than 1.54014…. In this paper, we give an improvement on this bound to and we investigate the parametric case as well. For those lists where the elements are preprocessed according to their sizes in non-increasing order, Csirik et al. (1983)  proved that no on-line algorithm can have an asymptotic performance ratio smaller than . We improve this result to . [Copyright &y& Elsevier]

Abstract: The utilization of populations is one of the most important features of evolutionary algorithms (EAs). There have been many studies analyzing the impact of different population sizes on the performance of EAs. However, most of such studies are based on computational experiments, except for a few cases. The common wisdom so far appears to be that a large population would increase the population diversity and thus help an EA. Indeed, increasing the population size has been a commonly used strategy in tuning an EA when it did not perform as well as expected for a given problem. He and Yao (2002)  showed theoretically that for some problem instance classes, a population can help to reduce the runtime of an EA from exponential to polynomial time. This paper analyzes the role of population further in EAs and shows rigorously that large populations may not always be useful. Conditions, under which large populations can be harmful, are discussed in this paper. Although the theoretical analysis was carried out on one multimodal problem using a specific type of EAs, it has much wider implications. The analysis has revealed certain problem characteristics, which can be either the problem considered here or other problems, that lead to the disadvantages of large population sizes. The analytical approach developed in this paper can also be applied to analyzing EAs on other problems. [Copyright &y& Elsevier]

Abstract: The advent of high throughput technologies, in particular microarrays, for biological research has revived interest in clustering, resulting in a plethora of new clustering algorithms. However, model selection, i.e., the identification of the correct number of clusters in a dataset, has received relatively little attention. Indeed, although central for statistics, its difficulty is also well known. Fortunately, a few novel techniques for model selection, representing a sharp departure from previous ones in statistics, have been proposed and gained prominence for microarray data analysis. Among those, the stability-based methods are the most robust and best performing in terms of prediction, but the slowest in terms of time. It is very unfortunate that as fascinating and classic an area of statistics as model selection, with important practical applications, has received very little attention in terms of algorithmic design and engineering. In this paper, in order to partially fill this gap, we make the following contributions: (A) the first general algorithmic paradigm for stability-based methods for model selection; (B) reductions showing that all of the known methods in this class are an instance of the proposed paradigm; (C) a novel algorithmic paradigm for the class of stability-based methods for cluster validity, i.e., methods assessing how statistically significant is a given clustering solution; (D) a general algorithmic paradigm that describes heuristic and very effective speed-ups known in the literature for stability-based model selection methods. Since the performance evaluation of model selection algorithms is mainly experimental, we offer, for completeness and without even attempting to be exhaustive, a representative synopsis of known experimental benchmarking results that highlight the ability of stability-based methods for model selection and the computational resources that they require for the task. As a whole, the contributions of this paper generalize in several respects reference methodologies in statistics and show that algorithmic approaches can yield deep methodological insights into this area, in addition to practical computational procedures. [Copyright &y& Elsevier]

Abstract: This paper discusses a model of constraint satisfaction problems known as uniquely extendible constraint satisfaction problems. This model includes and generalizes XOR-SAT, and the model includes an NP-complete problem that appears to share many of the threshold characteristics of random SAT. In this paper we find an exact threshold in the behavior of two versions of DPLL on random instances of this problem. One version uses the unit clause heuristic, and the other uses the generalized unit clause heuristic. Specifically, for DPLL with the unit clause heuristic, we prove that there is a clause density , smaller than the satisfiability threshold, such that for random instances with density smaller than this threshold, DPLL with unit clause will find a satisfying assignment in linear time, with uniformly positive probability. However, for random instances with density larger than this threshold, DPLL with unit clause will require exponential time, with uniformly positive probability, to find a satisfying assignment. We then find the equivalent threshold density for DPLL with the generalized unit clause heuristic. We also prove the analog of the -SAT Conjecture for this class of problems. [Copyright &y& Elsevier]

Many networking applications require timely access to recent network measurements, which can be captured using a sliding window model. Maintaining such measurements is a challenging task due to the fast line speed and scarcity of fast memory in routers. In this work, we study the impact of allowing slack in the window size on the asymptotic requirements of sliding window problems. That is, the algorithm can dynamically adjust the window size between W and W (1 + τ) where τ is a small positive parameter. We demonstrate this model's attractiveness by showing that it enables efficient algorithms to problems such as Maximum and General-Summing that require Ω (W) bits even for constant factor approximations in the exact sliding window model. Additionally, for problems that admit sub-linear approximation algorithms such as Basic-Summing and Count-Distinct , the slack model enables a further asymptotic improvement. The main focus of the paper is on the widely studied Basic-Summing problem of computing the sum of the last W integers from { 0 , 1 ... , R } in a stream. While it is known that Ω (W log ⁡ R) bits are needed in the exact window model, we show that approximate windows allow an exponential space reduction for constant τ. Specifically, for τ = Θ (1) , we present a space lower bound of Ω (log ⁡ (R W)) bits. Additionally, we show an Ω (log ⁡ (W / ϵ)) lower bound for RWϵ additive approximations and a Ω (log ⁡ (W / ϵ) + log ⁡ log ⁡ R) bits lower bound for (1 + ϵ) multiplicative approximations. Our work is the first to study this problem in the exact and additive approximation settings. For all settings, we provide memory optimal algorithms that operate in worst case constant time. This strictly improves on the work of [17] for (1 + ϵ) -multiplicative approximation that requires O (ϵ − 1 log ⁡ (R W) log ⁡ log ⁡ (R W)) space and performs updates in O (log ⁡ (R W)) worst case time. Finally, we show asymptotic improvements for the Count-Distinct , General-Summing , and Maximum problems. [ABSTRACT FROM AUTHOR]

A proper (simple) relation algebra is a collection A of binary relations on a set U such that the top element of the algebra is U × U , and A is closed under union, intersection, complementation, composition, converse and contains the identity relation on U. Proper relation algebras can be constructed using U = Z / p Z as a base set using a method due to Comer. The cycle structure of such an algebra must, in general, be determined a posteriori , normally with the aid of a computer. In this paper, we give an improved algorithm for checking the cycle structure that reduces the time complexity from O (p 2) to O (p). [ABSTRACT FROM AUTHOR]

In Temporal Logic (TL), a well-formed formula is generally formed by applying rules of its syntax finitely many times. However, under some circumstances, although formulas such as ones expressed by index set expressions , are constructed via applying rules of the syntax infinitely many times, they are possibly still well-formed since their equivalent concise syntax formulas can be found. With this motivation, this paper investigates the relationship between formulas specified by index set expressions and concise syntax by means of fixed-point approach. Firstly, we present two kinds of formulas, namely ⋁ i ∈ N 0 ◯ i Q and ⋁ i ∈ N 0 Q i , and prove they are indeed well-formed by proving they are equivalent to formulas ◇ Q and Q ⁎ respectively. Further, we generalize ⋁ i ∈ N 0 ◯ i Q to ⋁ i ∈ N 0 P (i) ∧ ◯ i Q and explore the least and greatest fixed-points of an abstract equation X ≡ Q ∨ P ∧ ◯ X. Based on these, some well-formed special instances of ⋁ i ∈ N 0 P (i) ∧ ◯ i Q are obtained. Besides, with the index set expression technique, we equivalently represent ' U ' (strong until) and ' W ' (weak until) constructs of propositional Linear Temporal Logic (LTL) within Propositional Projection Temporal Logic (PPTL). [ABSTRACT FROM AUTHOR]

In this paper, we study the k -forest problem in the model of resource augmentation. In the k -forest problem, given an edge-weighted graph G (V , E) , a parameter k , and a set of m demand pairs ⊆ V × V , the objective is to construct a minimum-cost subgraph that connects at least k demands. The problem is hard to approximate—the best-known approximation ratio is O (min ⁡ { | V | , k }). Furthermore, k -forest is as hard to approximate as the notoriously-hard densest k -subgraph problem. While the k -forest problem is hard to approximate in the worst-case, we show that with the use of resource augmentation, we can efficiently approximate it up to a constant factor. First, we restate the problem in terms of the number of demands that are not connected. In particular, the objective of the k -forest problem can be viewed as to remove at most m − k demands and find a minimum-cost subgraph that connects the remaining demands. We use this perspective of the problem to explain the performance of our algorithm (in terms of the augmentation) in a more intuitive way. Specifically, we present a polynomial-time algorithm for the k -forest problem that, for every ε > 0 , removes at most m − k demands and has cost no more than O (1 / ε 2) times the cost of an optimal algorithm that removes at most (1 − ε) (m − k) demands. [ABSTRACT FROM AUTHOR]

This paper deals with the conversion of expressions denoting Hadamard series into weighted rotating automata. We prove that any algorithm converting rational series into one-way weighted automata can be extended to provide an algorithm which achieves our goal. We apply this to define the derivation and the follow automata of a Hadamard expression. Our method may also be used to extend algorithms which perform the inverse conversion, but it is required to enhance the algorithm to fulfil some constraints. [ABSTRACT FROM AUTHOR]

For the underlying graph G of a network, k (⩾ 2) spanning trees of G are called completely independent spanning trees (CISTs for short) if they are mutually inner-node-disjoint. It is well-known that determining the existence of k CISTs in a graph is an NP-hard problem, even for k = 2. Also, there exists a k -connected graph which does not possess two CISTs for any k ⩾ 2. Accordingly, researches focused on the problem of constructing multiple CISTs in some particular famous networks. Pai and Chang (2016) proposed a unified approach to recursively construct two CISTs with diameter 2 n − 1 in several n -dimensional hypercube-variant networks for n ⩾ 4 , including locally twisted cubes L T Q n and crossed cubes C Q n. Later on, new constructions showed that the diameter of two CISTs can be reduced to 2 n − 2 if n = 4 and 2 n − 3 if n ⩾ 5 for L T Q n , and to 2 n − 2 if n = 4 , 5 and 2 n − 3 if n ⩾ 6 for C Q n. In this paper, we intend to construct more CISTs for those networks that are paid attention. We develop a novel tree searching algorithm, called two-stages tree-searching algorithm (abbreviated as TS 2), which can be used to construct three CISTs of a 6-regular graph if the scale of the graph is not too large and there exist three CISTs for certain. In particular, we demonstrate that three CISTs of L T Q 6 and C Q 6 can be acquired by using TS 2. Moreover, for high-dimensional L T Q n and C Q n with n ⩾ 7 , we show that their three CISTs can be constructed by recursion. Consequently, we obtain the following results: (i) For L T Q n , the diameters of three CISTs we constructed are 11, 12 and 12 when n = 6 , and all are 2 n − 1 when n ⩾ 7 ; (ii) For C Q n , all diameters of three CISTs we constructed are 12 when n = 6 , and 2 n + 1 when n ⩾ 7. [ABSTRACT FROM AUTHOR]

We consider networks of processes which interact with beeps. In the basic model defined by Cornejo and Kuhn [8] , which we refer to as the BL variant, processes can choose in each round either to beep or to listen. Those who beep are unable to detect simultaneous beeps. Those who listen can only distinguish between silence and the presence of at least one beep. Beeping models are weak in essence and even simple tasks may become difficult or unfeasible with them. In this paper, we address the problem of computing how many participants there are in a one-hop network: the counting problem. We first observe that no algorithm can compute this number with certainty in BL , even if it is randomised (Las Vegas). We thus consider the stronger variant where beeping nodes are able to detect simultaneous beeps, referred to as B c d L (cd stands for collision detection). We prove that at least n rounds are necessary in B c d L , and we present an algorithm whose running time is O (n) rounds with high probability. Further experimental results show that its expected running time is less than 10 n. Finally, we discuss how this algorithm can be adapted in other beeping models. In particular, we show that the algorithm can be emulated in BL , at the cost of a logarithmic slowdown and of trading its Las Vegas nature (certain result, uncertain time) against a Monte Carlo one (certain time, uncertain result). [ABSTRACT FROM AUTHOR]

Abstract We study the parameterized complexity of domination problems on sparse graphs and beyond. The nowhere dense classes of graphs have been proposed as the main model for sparseness that can be utilized algorithmically. The class of d -degenerate graphs is not nowhere dense, yet domination remains fixed-parameter tractable. Both nowhere dense classes of graphs and d -degenerate graph classes are biclique-free classes, meaning there is an integer t such that no graph in the class contains K t , t as a subgraph. In this paper we show that various domination problems are fixed-parameter tractable on biclique-free classes of graphs. Our algorithms are simple and rely on results from extremal graph theory that bound the number of edges in a t -biclique free graph. In particular, the problems k -Dominating Set , Connected k -Dominating Set , Independent k -Dominating Set and Minimum Weight k -Dominating Set are shown to be FPT, when parameterized by t + k , on graphs not containing K t , t as a subgraph. With the exception of Connected k -Dominating Set all described algorithms are linear in the size of the input graph. [ABSTRACT FROM AUTHOR]

Highlights • Algorithms for covering and hitting a given set of line segments by two congruent squares of minimum size is studied. • The algorithm produces optimum solution by sequentially reading the input array (read only) twice. • The extra space complexity of the algorithm is O (1). • A restricted version of covering is also studied where each object is to be completely covered by at least one square. • This algorithm gives 2 approximation result to cover/hit the segments with two congruent disks of minimum size. Abstract This paper discusses the problem of covering and hitting a set of line segments L in R 2 by a pair of axis-parallel congruent squares of minimum size. We also discuss the restricted version of covering, where each line segment in L is to be covered completely by at least one square. The proposed algorithms assume that the input segments are given in a read-only array. For each of these problems (i.e. covering , hitting and restricted covering problems), our proposed algorithm reports the optimum result by executing only two passes of reading the input array sequentially. All these algorithms need only O (1) extra space. The solution of these problems also give a 2 approximation for covering and hitting those line segments L by two congruent disks of minimum radius with same computational complexity. [ABSTRACT FROM AUTHOR]

Abstract Let G = (A ∪ P , E) be a bipartite graph where A denotes a set of applicants, P denotes a set of posts and ranks on the edges denote preferences of the agents over posts. A matching M in G is rank-maximal if it matches the maximum number of applicants to their top-rank post, subject to this, the maximum number of applicants to their second rank post and so on. In this paper, we develop a switching graph characterization of rank-maximal matchings, which is a useful tool that encodes all rank-maximal matchings in an instance. The characterization leads to simple and efficient algorithms for several interesting problems. In particular, we give an efficient algorithm to compute the set of rank-maximal pairs in an instance. We show that the problem of counting the number of rank-maximal matchings is # P -complete and also give an FPRAS for the problem. Finally, we consider the problem of deciding whether a rank-maximal matching is popular among all the rank-maximal matchings in a given instance, and give an efficient algorithm for the problem. [ABSTRACT FROM AUTHOR]

Abstract Identifying the most influential spreaders is an important issue for the study of the dynamics of information diffusion in complex networks. In this paper we analyze the following spreading model. Initially, a few nodes know a piece of information and are active spreaders of it. At subsequent rounds, spreaders communicate the information to their neighbors. Upon receiving the information, a node becomes aware of it but does not necessarily become a spreader; it starts spreading only if it gets the information from a sufficiently large number of its neighbors. A set of initial spreaders that guarantees that all the nodes become aware of the information is called a perfect seed set. We study the problem of choosing a perfect seed set of minimum size. We provide hardness results and show that the problem becomes tractable on trees. In case of general graphs, we provide an efficient algorithm and validate its effectiveness (in terms of the solution size) on real-life networks. We also study perfect seed sets in dense graphs and derive a bound on the size of a dominating set in Ore graphs. [ABSTRACT FROM AUTHOR]

Abstract A locally connected spanning tree (LCST) T of a graph G is a spanning tree of G such that, for each node, its neighborhood in T induces a connected subgraph in G. The problem of determining whether a graph contains an LCST or not has been proved to be NP-complete, even if the graph is planar or chordal. The main result of this paper is a simple linear time algorithm that, given a maximal planar chordal graph, determines in linear time whether it contains an LCST or not, and produces one if it exists. We give an analogous result for the case when the input graph is a maximal outerplanar graph. [ABSTRACT FROM AUTHOR]

Abstract The sensitivity conjecture proposed by Nisan and Szegedy in 1994, which asserts that for any Boolean function, its sensitivity complexity is polynomially related to the block sensitivity complexity, is one of the most important and challenging problems in the study of decision tree complexity. Despite a lot of efforts, the best known upper bound of block sensitivity, as well as the certificate complexity, is still exponential in terms of sensitivity. In this paper, we give a better upper bound for certificate complexity and block sensitivity, b s (f) ≤ C (f) ≤ (8 9 + o (1)) s (f) 2 s (f) − 1 , where b s (f) , C (f) and s (f) are the block sensitivity, certificate complexity and sensitivity, respectively. The proof is based on a deep investigation on the structure of the sensitivity graph. We also provide a tighter relationship between the 0-certificate complexity C 0 (f) and 0-sensitivity s 0 (f) for functions with small 1-sensitivity s 1 (f). [ABSTRACT FROM AUTHOR]

Abstract We consider the problem of scheduling complex-valued demands over a discretized time horizon. Given a set of users, each user is associated with a set of demands representing different power consumption preferences. A demand is represented by a complex number, a time interval, and a utility value obtained if it is satisfied. At each time slot, the magnitude of the total selected demands should not exceed a given generation capacity. This naturally captures the supply constraints in alternating current (AC) electric systems. In this paper, we consider maximizing the aggregate user utility subject to power supply limits over a time horizon. We present approximation algorithms characterized by the maximum angle ϕ between any two complex-valued demands. More precisely, a PTAS is presented for the case ϕ ∈ [ 0 , π 2 ] , a bi-criteria FPTAS for ϕ ∈ [ 0 , π - ε ] for any polynomially small ε , assuming the number of time slots in the discretized time horizon is a constant. Furthermore, if the number of time slots is part of the input, we present a reduction to the real-valued unsplittable flow problem on a path with only a constant approximation ratio. Finally, we present a practical greedy algorithm for the single time slot case with an approximation ratio of 1 2 cos ⁡ ϕ 2 and a running time complexity of only O (N log ⁡ N) , N standing for the aggregate number of user demands, which can be implemented efficiently in practice. [ABSTRACT FROM AUTHOR]

Abstract Real-world networks, like social networks or the internet infrastructure, have structural properties such as large clustering coefficients that can best be described in terms of an underlying geometry. This is why the focus of the literature on theoretical models for real-world networks shifted from classic models without geometry, such as Chung–Lu random graphs, to modern geometry-based models, such as hyperbolic random graphs. With this paper we contribute to the theoretical analysis of these modern, more realistic random graph models. Instead of studying directly hyperbolic random graphs, we use a generalization that we call geometric inhomogeneous random graphs (GIRGs). Since we ignore constant factors in the edge probabilities, GIRGs are technically simpler (specifically, we avoid hyperbolic cosines), while preserving the qualitative behavior of hyperbolic random graphs, and we suggest to replace hyperbolic random graphs by this new model in future theoretical studies. We prove the following fundamental structural and algorithmic results on GIRGs. (1) We provide a sampling algorithm that generates a random graph from our model in expected linear time, improving the best-known sampling algorithm for hyperbolic random graphs by a substantial factor O (n). (2) We establish that GIRGs have clustering coefficients in Ω (1) , (3) we prove that GIRGs have small separators, i.e., it suffices to delete a sublinear number of edges to break the giant component into two large pieces, and (4) we show how to compress GIRGs using an expected linear number of bits. Highlights • GIRGs are a random graph model that reproduces many features of real-world networks. • The model contains the celebrated hyperbolic random graphs as special case. • They have large clustering coefficient, small separators, and small entropy. • We present a linear-time sampling algorithm and a linear-space compression algorithm. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider the problem of connected edge searching of weighted trees. Barrière et al. claim in [L. Barrière, P. Flocchini, P. Fraigniaud, N. Santoro, Capture of an intruder by mobile agents, in: SPAA’02: Proceedings of the Fourteenth Annual ACM Symposium on Parallel Algorithms and Architectures, ACM, New York, NY, USA, 2002, pp. 200–209] that there exists a polynomial-time algorithm for finding an optimal search strategy, that is, a strategy that minimizes the number of used searchers. However, due to some flaws in their algorithm, the problem turns out to be open. It is proven in this paper that the considered problem is strongly NP-complete even for node-weighted trees (the weight of each edge is 1) with one vertex of degree greater than 2. It is also shown that there exists a polynomial-time algorithm for finding an optimal connected search strategy for a given bounded degree tree with arbitrary weights on the edges and on the vertices. This is an FPT algorithm with respect to the maximum degree of a tree. [Copyright &y& Elsevier]

Abstract: We introduce a comprehensive hybrid failure model for synchronous distributed systems, which extends a conventional hybrid process failure model by adding communication failures: Every process in the system is allowed to commit up to send link failures and experience up to receive link failures per round here, without being considered faulty; up to some and among those may even cause erroneous messages rather than just omissions. In a companion paper (Schmid et al. (2009) ), devoted to a complete suite of related impossibility results and lower bounds, we proved that this model surpasses all existing link failure modeling approaches in terms of the assumption coverage in a simple probabilistic setting. In this paper, we show that several well-known synchronous consensus algorithms can be adapted to work under our failure model, provided that the number of processes required for tolerating process failures is increased by small integer multiples of , , , . This is somewhat surprising, given that consensus in the presence of unrestricted link failures and mobile (moving) process omission failures is impossible. We provide detailed formulas for the required number of processes and rounds, which reveal that the lower bounds established in our companion paper are tight. We also explore the power and limitations of authentication in our setting, and consider uniform consensus algorithms, which guarantee their properties also for benign faulty processes. [Copyright &y& Elsevier]

Abstract: Faugère’s algorithm is one of the fastest algorithms to compute Gröbner bases. It uses two criteria namely the criterion and the IsRewritten criterion to detect the useless critical pairs (see Faugère (2002) ). The IsRewritten criterion has been used in the algorithm, but it has not been explicitly declared in the related paper. In this paper, we give first a complete proof for the IsRewritten criterion and then using a signature structure on Buchberger’s algorithm, we apply this criterion on Buchberger’s algorithm. We have implemented a new algorithm (based on the above results) in Maple to compute a Gröbner basis of a general ideal and we evaluate its performance via some examples. [Copyright &y& Elsevier]

Abstract: A snap-stabilizing protocol, starting from any configuration, always behaves according to its specification. In this paper, we are interested in the message forwarding problem in a message-switched network in which the system resources must be managed in order to deliver messages to any processor of the network. To this end, we use the information provided by a routing algorithm. In the context of an arbitrary initialization (due to stabilization), this information may be corrupted. In Cournier et al. (2009) , we show that there exist snap-stabilizing algorithms for this problem (in the state model). This implies that we can request the system to begin forwarding messages without losses even if routing information is initially corrupted. In this paper, we propose another snap-stabilizing algorithm for this problem which improves the space complexity of the one in Cournier et al. (2009) . [Copyright &y& Elsevier]

Abstract: Compression algorithms based on Burrows–Wheeler transform (BWT) take advantage of the fact that the word output of BWT shows a local similarity and then turns out to be highly compressible. The aim of the present paper is to study such “clustering effect” by using notions and methods from Combinatorics on Words. The notion of balance of a word plays a central role in our investigation. Empirical observations suggest that balance is actually the combinatorial property of input word that ensure optimal BWT compression. Moreover, it is reasonable to assume that the more balanced the input word is, the more local similarity we have after BWT (and therefore the better the compression is). This hypothesis is here corroborated by experiments on “real” text, by using local entropy as a measure of the degree of balance of a word. In the setting of Combinatorics on Words, a sound confirmation of previous hypothesis is given by a result of Mantaci et al. (2003) , which states that, in the case of a binary alphabet, there is an equivalence between circularly balanced words, words having a clusterized BWT, and the conjugates of standard words. In the case of alphabets of size greater than two, there is no more equivalence. The last section of the present paper is devoted to investigate the relationships between these notions, and other related ones (as, for instance, palindromic richness) in the case of a general alphabet. [Copyright &y& Elsevier]

Abstract: Any mathematical theory of algorithms striving to offer a foundation for programming needs to provide a rigorous definition for an abstract algorithm. The works reported by Girard (1988) in  and by Moschovakis (1989, 1995) in  are among the best examples of such attempts. They both try to offer a mathematically precise and rigorous formulation of an abstract algorithm, intend to keep the algorithmic flavour present and take the notion of recursion as primary and central. The present work is motivated by Girard’s GoI 2 paper (Girard (1988) , which offers a treatment of recursion in terms of fixed points of linear functions. It is situated in the context of the geometry of interaction (GoI) program and is carried out in the concrete setting of the space of bounded linear maps on a Hilbert space. In this paper, we extend the work in Girard (1988)  to the context of traced unique decomposition categories, once again emphasizing the role of abstract trace in the theory of computing. We show that traced unique decomposition categories enriched over partially additive monoids or their variations suffice to axiomatize and hence extend the work in Girard’s GoI 2 paper. The theory developed here allows us to formulate an abstract notion of an algorithm as a pair of morphisms in a traced unique decomposition category, an abstract notion of computation as the execution formula (defined using the trace operator) applied to an algorithm, and finally a notion of deadlock-freeness for algorithms. In addition, we can treat recursive definitions, fixed points and fixed point operators in a uniform way in terms of traced unique decomposition categories. [Copyright &y& Elsevier]

Abstract: In the past, research on multiple criteria scheduling assumes that the number of available machines is fixed during the whole scheduling horizon and research on scheduling with limited machine availability assumes that there is only a single criterion that needs to be optimized. Both assumptions may not hold in real life. In this paper we simultaneously consider both bicriteria scheduling and scheduling with limited machine availability. We focus on two parallel machines’ environment and the goal is to find preemptive schedules to optimize both makespan and total completion time subject to machine availability. Our main contribution in this paper is that we showed three bicriteria scheduling problems are in P by providing polynomial time optimal algorithms. [Copyright &y& Elsevier]

Abstract: Computability logic (CoL) is a recently introduced semantical platform and research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally been. Formulas in CoL stand for interactive computational problems, seen as games between a machine and its environment; logical operators represent operations on such entities; and “truth” is understood as existence of an effective solution, i.e., of an algorithmic winning strategy. The formalism of CoL is open-ended, and may undergo series of extensions as the studies of the subject advance. Propositional connectives and quantifiers in it come in a variety of indispensable versions. So far three sorts of conjunction and disjunction–parallel, sequential and choice–have been studied, with the first and the third sorts being reminiscent of the multiplicative and additive operators of linear logic, respectively. The present paper adds one more natural kind to this collection, termed toggling. The toggling operations can be characterized as lenient versions of choice operations where choices are retractable, being allowed to be reconsidered any finite number of times. This way, they model trial-and-error style decision steps in interactive computation. The main technical result of this paper is constructing a sound and complete axiomatization for the propositional fragment of computability logic whose vocabulary includes all four kinds of conjunction and disjunction: parallel, toggling, sequential and choice, together with negation. Along with toggling conjunction and disjunction, the paper also introduces the toggling versions of quantifiers and recurrence (“exponential”) operations. [Copyright &y& Elsevier]

Abstract: In this paper the minimum spanning tree problem with uncertain edge costs is discussed. In order to model the uncertainty a discrete scenario set is specified and a robust framework is adopted to choose a solution. The min–max, min–max regret and 2-stage min–max versions of the problem are discussed. The complexity and approximability of all these problems are explored. It is proved that the min–max and min–max regret versions with nonnegative edge costs are hard to approximate within for any unless the problems in NP have quasi-polynomial time algorithms. Similarly, the 2-stage min–max problem cannot be approximated within unless the problems in NP have quasi-polynomial time algorithms. In this paper randomized LP-based approximation algorithms with performance bound of for min–max and 2-stage min–max problems are also proposed. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a fixed-parameter algorithm for the tree edit distance problem for unordered trees under the unit cost model that works in time and space, where the parameter is the maximum bound of the edit distance and is the maximum size of input trees. This paper also presents polynomial-time algorithms for the case where the maximum degree of the largest common subtree is bounded by a constant. [ABSTRACT FROM AUTHOR]

Abstract Airline network, including airports as network nodes and flight routes as directed network edges, has a lot of special features such as departure and arrival times, air ticket budget, flight capacity, transportation cost, etc. Thus, analyzing network behavior and service performance for such a network is much more difficult than that for many other networks. In this paper, taking China domestic airline network as a representative, we try to discuss the reachability issue for each airport respectively, which could reflect its regional connectivity level and service quality of civil aviation. More specifically, we evaluate reachability through many features including node degree, betweenness, closeness, etc. To get the values of some features, we design a fast Dijkstra-based all-pair shortest path algorithm with both time and budget requirements, then use Fenwick Tree to further improve the time efficiency. Actually, it is a shortest path problem with time windows and other constraints. Furthermore, we propose a faster solution by reducing the edges in the duplicated graph as a simplification and then provide the time complexity proof. Finally, we implement Analytic Hierarchy Process (AHP) to convert the reachability feature into numerical values for all airports to measure their service qualities precisely. Our results for China domestic airline network with 210 airports and 69,160 flight routes will definitely become a guide to airline companies and civil aviation administration for their further development and management. [ABSTRACT FROM AUTHOR]

Abstract In this paper we study a variant of the p -center problem on cactus graphs in which the p -center are asked to be connected, and this problem is called the connected p -center problem. For the connected p -center problem on cactus graphs, we propose a dynamic programming algorithm and show that the time complexity is O (n 2 p 2) , where n is the number of the vertices of the cactus graphs. [ABSTRACT FROM AUTHOR]

Abstract We discuss algorithmic issues on the well-known paper-and-pencil game RaceTrack. On a very simple track called Indianapolis, we introduce the problem and simple approaches, which we then extend to more complex tracks. We present and experimentally evaluate efficient algorithms for single player scenarios. We also consider a variant where the parts of the track are known as soon as they become visible during the race. [ABSTRACT FROM AUTHOR]

Abstract: The paper 1 [1] Supported by Engineering and Physical Sciences Research Council (EPSRC), U.K., grant EP/F014406/1. develops a technique for computation inference rules admissible in temporal logic . The problem whether there exists an algorithm recognizing inference rules admissible in is a long-standing open problem. The logic has neither the extension property nor the co-cover property which previously were central instruments for construction decision algorithms for admissibility in modal logics (e.g. reflexive and transitive modal logic ). Our paper uses a linear-compression property, a zigzag-ray property and a zigzag stretching property which hold for . The main result of the paper is a sufficient condition for admissibility inference rules in . It is shown that all rules which are valid in special finite models (with an effective upper bound on size) must be admissible in . [Copyright &y& Elsevier]

Abstract: The frequent connected subgraph mining problem, i.e., the problem of listing all connected graphs that are subgraph isomorphic to at least a certain number of transaction graphs of a database, cannot be solved in output polynomial time in the general case. If, however, the transaction graphs are restricted to forests then the problem becomes tractable. In this paper we generalize the positive result on forests to graphs of bounded tree-width. In particular, we show that for this class of transaction graphs, frequent connected subgraphs can be listed in incremental polynomial time. Since subgraph isomorphism remains NP-complete for bounded tree-width graphs, the positive complexity result of this paper shows that efficient frequent pattern mining is possible even for computationally hard pattern matching operators. [Copyright &y& Elsevier]

Abstract: The paper applies the method of defensive forecasting, based on the use of game-theoretic supermartingales, to prediction with expert advice. In the traditional setting of a countable number of experts and a finite number of outcomes, the Defensive Forecasting Algorithm is very close to the well-known Aggregating Algorithm. Not only the performance guarantees but also the predictions are the same for these two methods of fundamentally different nature. The paper also discusses a new setting where the experts can give advice conditional on the learner’s future decision. Both the algorithms can be adapted to the new setting and give the same performance guarantees as in the traditional setting. Finally, an application of defensive forecasting to a setting with several loss functions is outlined. [Copyright &y& Elsevier]

Abstract: This paper establishes an axiomatic foundation and a representation theorem for the rigorous, constructive process, called sequence-based specification, of deriving precise specifications from ordinary (informal) statements of functional requirements. The representation theorem targets a special class of Mealy state machines, and algorithms are presented for converting from the set of sequences that define the specification to the equivalent Mealy machine, and vice versa. Since its inception, sequence-based specification has been effectively used in a variety of real applications, with gains reported in quality and productivity. This paper establishes the mathematical foundation independently of the process itself. [Copyright &y& Elsevier]

Abstract: The -set agreement problem is a generalization of the uniform consensus problem: each process proposes a value, and each non-faulty process has to decide a value such that a decided value is a proposed value, and at most different values are decided. It has been shown that any algorithm that solves the -set agreement problem in synchronous systems that can suffer up to crash failures requires rounds in the worst case. It has also been shown that it is possible to design early deciding algorithms where no process decides and halts after rounds, where is the number of actual crashes in a run (). This paper explores a new direction to solve the -set agreement problem in a synchronous system. It considers that the system is enriched with base objects (denoted has _SA objects) that allow solving the -set agreement problem in a set of processes (). The paper makes several contributions. It first proposes a synchronous -set agreement algorithm that benefits from such underlying base objects. This algorithm requires rounds, more precisely, rounds, where . The paper then shows that this bound, that involves all the parameters that characterize both the problem () and its environment (, and ), is a lower bound. The proof of this lower bound sheds additional light on the deep connection between synchronous efficiency and asynchronous computability. Finally, the paper extends its investigation to the early deciding case. It presents a -set agreement algorithm that directs the processes to decide and stop by round . These bounds generalize the bounds previously established for solving the -set agreement problem in pure synchronous systems. [Copyright &y& Elsevier]

Abstract: Recently, there has been significant theoretical progress towards fixed-parameter algorithms for the DOMINATING SET problem of planar graphs. It is known that the problem on a planar graph with vertices and dominating number can be solved in time using tree/branch-decomposition based algorithms. In this paper, we report computational results of Fomin and Thilikos algorithm which uses the branch-decomposition based approach. The computational results show that the algorithm can solve the DOMINATING SET problem of large planar graphs in a practical time and memory space for the class of graphs with small branchwidth. For the class of graphs with large branchwidth, the size of instances that can be solved by the algorithm in practice is limited to about one thousand edges due to a memory space bottleneck. The practical performances of the algorithm coincide with the theoretical analysis of the algorithm. The results of this paper suggest that the branch-decomposition based algorithms can be practical for some applications on planar graphs. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a restricted variant of the scheduling problem, where the machines are the strategic players. For this multi-parameter mechanism design problem, the only known truthful mechanisms use task independent allocation algorithms and only have approximation ratio [N. Nisan, A. Ronen. Algorithmic mechanism design (extended abstract), in: STOC’99: Proceedings of the thirty-first annual ACM symposium on Theory of computing, ACM, New York, NY, USA, 1999. pp. 129–140; A. Mu’alem, M. Schapira, Setting lower bounds on truthfulness: Extended abstract, in: SODA’07: Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2007, pp. 1143–1152; P. Lu, C. Yu, An improved randomized truthful mechanism for scheduling unrelated machines, in: 25th International Symposium on Theoretical Aspects of Computer Science, STACS, 2008, pp. 527–538; P. Lu, C. Yu, Randomized truthful mechanisms for scheduling unrelated machines, in: C.H. Papadimitriou, S. Zhang (Eds.), Proceedings of WINE, in: Lecture Notes in Computer Science, vol. 5385, Springer, 2008, pp. 402–413]. Lavi and Swamy first use the cycle monotone condition and design a 3-approximation truthful mechanism for a two value variant in [R. Lavi, C. Swamy, Truthful mechanism design for multi-dimensional scheduling via cycle monotonicity, in: EC’07: Proceedings of the 8th ACM conference on Electronic commerce, ACM, New York, NY, USA, 2007, pp. 252–261], where the processing time of task on machine , say , can only be either a lower value or a higher value . We consider a generalized variant, where lies in and is a parameter satisfying some condition. We consider two special cases, case A when , and case B when ,, and give randomized truthful mechanisms with approximation ratio for both cases. Based on these two cases’ results, we are also able to deal with the general case of our two-range-values scheduling problem. We use a combination of two mechanisms, which is also a novel method in mechanism design for scheduling problems, and finally we give a randomized truthful mechanism with approximation ratio . Although the generalization seems a little incremental, we actually use a very novel technique in the key step of proving truthfulness for case A, as well as a new mechanism scheme for case B. Besides, the results in this paper are the first truthful mechanisms with constant approximation ratios when a machine (player) can report infinitely possible values, which is quite different from the two value variant, in which only finite values are available. Furthermore, together with Lavi and Swamy’s work, our results suggest that such a task-dependent approach can really do much better for the scheduling unrelated machines problem. [Copyright &y& Elsevier]

Abstract: In this paper, we show that it can be tested in polynomial time as to whether a scenario is an execution of a Petri net. This holds for a wide variety of Petri net classes, ranging from elementary nets to general inhibitor nets. Scenarios are given by causal structures expressing causal dependencies and concurrency among events. In the case of elementary nets and of place/transition nets, such causal structures are partial orders among transition occurrences. For several extended Petri net classes, the extension of partial orders to stratified order structures is considered. The algorithms are based on the representation of the non-sequential behavior of Petri nets by so-called token flow functions and a characterization of Petri net executions called token flow property. This property allows nontrivial transformations into flow optimization problems, which can be solved in polynomial time. The paper is a revised, consolidated and extended version of the conference papers [G. Juhás, R. Lorenz, J. Desel, Can I execute my scenario in your net?, in: G. Ciardo, P. Darondeau (Eds.), ICATPN, in: Lecture Notes in Computer Science, Springer, 2005, pp. 289–308; R. Lorenz, S. Mauser, R. Bergenthum, Testing the Executability of Scenarios in General Inhibitor Nets, in: ACSD, IEEE Computer Society, 2007, pp. 167–176] and includes parts of the habilitation thesis [R. Lorenz, Szenario-basierte Verifikation und Synthese von Perinetzen: Theorie und Anwendungen, Habilitation, 2006]. [Copyright &y& Elsevier]

Abstract: The -median problem on a tree is to find a set of vertices on that minimizes the sum of distances from ’s vertices to . In this paper, we study two generalizations of the 2-median problem, which are obtained by imposing constraints on the two vertices selected as a 2-median: one is to limit their distance while the other is to limit their eccentricity. Previously, both the best upper bounds of these two generalizations were [A. Tamir, D. Perez-Brito, J.A. Moreno-Perez, A polynomial algorithm for the -centdian problem on a tree, Networks 32 (1998) 255–262; B.-F. Wang, S.-C. Ku, K.-H. Shi, Cost-optimal parallel algorithms for the tree bisector problem and applications, IEEE Transactions on Parallel and Distributed Systems 12 (9) (2001) 888–898]. In this paper, we solve both in time. We also study cases when linear time algorithms exist for the two generalizations. For example, we solve both in linear time when edge lengths and vertex weights are all polynomially bounded integers. Furthermore, we consider the relaxation of the two generalized problems by allowing 2-medians on any position of edges, instead of just on vertices, and we give -time algorithms for them. A problem, named the tree marker problem, arises several times in our approaches to the two generalized 2-median problems, and we give an -time algorithm for this problem. We also use this algorithm to speedup an algorithm of Gupta and Punnen [S.K. Gupta, A.P. Punnen, Group center and group median of a tree, European Journal of Operational Research 65 (1993) 400–406] for the group median problem, improving the running time from to , where is the number of groups in the input. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to show how the rewriting-logic-based Real-Time Maude language and tool can be used to formally model, simulate, and model check advanced wireless sensor network (WSN) algorithms. This is done by first proposing some general techniques for modeling and analyzing WSN algorithms, and then by showing how these techniques have been applied to the modeling, performance estimation, and model checking of the state-of-the-art optimal geographical density control (OGDC) density control algorithm. Wireless sensor networks in general, and the OGDC algorithm in particular, pose many challenges to their formal specification and analysis, including novel communication forms, spatial entities, time-dependent and probabilistic features, and the need to analyze both correctness and performance. We focus on Monte Carlo simulations to evaluate the performance of OGDC. Extensive simulations with up to 800 sensor nodes, and comparison with the ns-2 simulations of OGDC, indicate that Real-Time Maude simulations provide fairly accurate performance estimates of WSN algorithms. As a consequence, simulating the high-level Real-Time Maude model of a WSN algorithm eliminates the need for implementing it on a simulation tool to get a faithful estimate of its performance, while providing much greater flexibility in defining the appropriate simulation scenario; in addition, Real-Time Maude model checking can search for “corner case” bugs and evaluate best-case and worst-case performance. Some of the techniques presented in this paper are also used in an ongoing analysis effort of another state-of-the-art WSN algorithm. [Copyright &y& Elsevier]

Abstract: Many applications need to solve the deadline guaranteed packet scheduling problem. However, it is a very difficult problem if three or more deadlines are present in a set of packets to be scheduled. The traditional approach to dealing with this problem is to use EDF (Earliest Deadline First) or similar methods. Recently, a non-EDF based algorithm was proposed that constantly produces a higher throughput than EDF-based algorithms by repeatedly finding an optimal scheduling for two classes. However, this new method requires the two classes be non-overloaded, which greatly restricts its applications. Since the overloaded situation is not avoidable from one iteration to the next in dealing with multiple classes, it is compelling to answer the open question: Can we find an optimal schedule for two overloaded classes efficiently? This paper first proves that this problem is NP-complete. Then, this paper proposes an optimal preprocessing algorithm that guarantees to drop a minimum number of packets from the two classes such that the remaining set is non-overloaded. This result directly improves on the new method. [Copyright &y& Elsevier]