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The paper considers the disadvantages of existing approaches to testing software and hardware data security tools in order to confirm compliance of the implemented functionality with the declared characteristics. It demonstrates the necessity of ensuring completeness and optimality of testing. The paper describes some testing approaches based on the development of mathematical models using the automata theory and ensuring completeness of testing, but leaving the question of its optimality open. It describes the approach proposed earlier by the authors, which ensures both completeness and optimality of testing using the graph theory. In accordance with this approach, the software and hardware data security tool is represented as a directed graph without loops or multiple edges. The graph vertices correspond to the states of the software or hardware component, and the directed edges correspond to the transitions of the data security tool from one state to another when performing non-target functions or security functions. On the basis of this approach, the authors propose an algorithm for solving the problem of testing software and hardware data security tools using a number of well-known algorithms on graphs. In the paper, it is substantiated that a solution to the problem of ensuring completeness and optimality of testing exists if and only if any vertex of the derived graph obtained by removing all unused vertices and edges either belongs to a directed chain or lies in a strongly connected component. Application of the proposed algorithm for solving the problem of testing one of the software and hardware security tools is considered, and the possibility of its application in practice is confirmed. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we empirically profile three algorithms for the Shortest Negative Cost Cycle (SNCC) problem. In this problem, we are given a directed, weighted graph G = 〈 V , E , c 〉 , and the goal is to identify a negative cost cycle with the fewest number of edges. The SNCC problem finds applications in a number of domains ranging from program verification to certifying algorithm design. The first polynomial time algorithm for this problem was proposed in Subramani (2009). Since then, several additional techniques, including a randomized approach, have been proposed for the SNCC problem. Our goal in this paper is to analyze three algorithmic paradigms for this problem from the empirical perspective. Towards this end, we profile these algorithmic approaches over a wide range of inputs. Our results indicated that the randomized algorithm is the algorithm of choice over a number of graph classes. [ABSTRACT FROM AUTHOR]

Abstract The paper is devoted to a Gram classification of an important class of signed graphs with loops playing an important role in many branches of mathematics, physics and computer science including game theory, crystallography, Diophantine geometry, Lie theory, spectral graph theory, a graph coloring technique, algebraic methods in graph theory. They have many deep applications in spectral machine learning methods, electrical networks, to link sign prediction in signed unipartite and bipartite networks, and community partition in social networks. We continue the study of finite connected edge-bipartite graphs Δ (bigraphs, for short), with m ≥ 2 vertices (a class of signed graphs), started in Simson (2013) and developed in Simson (2016) by means of the non-symmetric Gram matrix G ˇ Δ ∈ M m (Z) defining Δ , its symmetric Gram matrix G Δ : = 1 2 [ G ˇ Δ + G ˇ Δ t r ] ∈ M m (1 2 Z) , and the Gram quadratic form q Δ : Z m → Z. In the present paper, given n ≥ 1 , we mainly study connected principal Cox-regular edge-bipartite graphs Δ with loops and n + 1 ≥ 2 vertices, in the sense that the symmetric Gram matrix G Δ ∈ M n + 1 (Z) of Δ is positive semi-definite of rank n ≥ 1. Our aim is to classify such edge-bipartite graphs by means of an inflation algorithm, up to the weak Gram Z -congruence Δ ∼ Z Δ ′ , where Δ ∼ Z Δ ′ means that G Δ ′ = B t r ⋅ G Δ ⋅ B , for some B ∈ M n + 1 (Z) with det B = ± 1. Our main result of the paper asserts that, given a principal Cox-regular connected edge-bipartite graph Δ with n + 1 ≥ 2 vertices, there exists an edge-bipartite Euclidean graph D n + 1 of Tables A and B, and a suitably chosen sequence t • − of the inflation operators, each of one of the forms Δ ′ ↦ t a − Δ ′ or Δ ′ ↦ t a b − Δ ′ , such that the composite operator Δ ↦ t • − Δ reduces Δ to the bigraph D n + 1 such that: (i) Δ ∼ Z D n + 1 and (ii) the bigraphs Δ , and D n + 1 have the same number of loops. The algorithm does not change loops and computes a matrix B ∈ M n + 1 (Z) , with det B = ± 1 , defining the weak Gram Z -congruence Δ ∼ Z D n + 1 , that is, satisfying the equation G D n + 1 = B t r ⋅ G Δ ⋅ B. [ABSTRACT FROM AUTHOR]

Most recently, the large scale graphs with billions of edges and nodes have become quite prevalent and significant. These graphs are intensely being used in complex networks associated with the package of big data like social networks etc. some of common challenges associated with these graphs that hinder the performance of complex systems and needs to be addressed are the huge number of nodes and edges present in the data, diverse types of edges and nodes, significant amount of important information is not available and many clustering problems are NP-hard. As a matter of demand, analyzing and processing graphs has came up as a challenging issue faced by the big data researchers across the globe. In the light of the similar context, this research paper addresses and investigates validation techniques and methodology for various existing algorithms like edge betweenness, walktrap, leading eigen vector, and infomap for the datasets like Zachary karate club network and Immunograph. This research paper also proposed an algorithm namely random walk fast greedy and compared it with existing algorithms. The implementation has been carried out on R version 3.3.2. The authors have reported and analyzed the comparative performance characteristics of these algorithms promising to contribute towards the large scale graph community for complex systems and higher analytical inferences. The results achieved while implementation depicts markable improvement as compared with the current state of art techniques. [ABSTRACT FROM AUTHOR]

In this paper, we study the most basic domination invariants in graphs, in which number 2 is intrinsic part of their definitions. We classify them upon three criteria, two of which give the following previously studied invariants: the weak 2 -domination number, γ w 2 ( G ) , the 2 -domination number, γ 2 ( G ) , the { 2 } -domination number, γ { 2 } ( G ) , the double domination number, γ × 2 ( G ) , the total { 2 } -domination number, γ t { 2 } ( G ) , and the total double domination number, γ t × 2 ( G ) , where G is a graph in which the corresponding invariant is well defined. The third criterion yields rainbow versions of the mentioned six parameters, one of which has already been well studied, and three other give new interesting parameters. Together with a special, extensively studied Roman domination, γ R ( G ) , and two classical parameters, the domination number, γ ( G ) , and the total domination number, γ t ( G ) , we consider 13 domination invariants in graphs. In the main result of the paper we present sharp upper and lower bounds of each of the invariants in terms of every other invariant, a large majority of which are new results proven in this paper. As a consequence of the main theorem we obtain new complexity results regarding the existence of approximation algorithms for the studied invariants, matched with tight or almost tight inapproximability bounds, which hold even in the class of split graphs. [ABSTRACT FROM AUTHOR]

Calculating and analyzing the number of spanning trees of graphs (network models) is an important and interesting research project in wide variety of fields, such as mathematics, physics, theoretical computer science, chemistry and so on. The number of spanning trees of graphs (models) displays amounts of information on its structural features and also on some relevant dynamical properties, in particular network security, random walks and percolation. In this paper, firstly, due to lots of graphs (models) are built on the basis of various simple and small elements (components), we provide primarily some helpful network-operation, such as link-operation and merge-operation, to generate more realistic and complicated graphs (models). Secondly, considering reliability of fault-tolerance to random faults and of intrusion-tolerance to selectively remove attacks, synchronization capability and diffusion properties of networks, we present an iterative method (algorithm) for computing the total number of spanning trees. As a pellucid example, we apply our method to tree space and cycle space, notice that it is proved to be indeed a better tool. In order to reflect more widely practical meanings, we study its applications in graph theory, including ladder-graph with zero clustering coefficient, wheel-graph having nonzero clustering coefficient as constituent ingredients of maximal planar graphs. In the rest of this paper, we make a brief summary that the method described by us can be designed a program (algorithm) for obtaining easily the exact number of spanning trees of some models. [ABSTRACT FROM AUTHOR]

A circulant graph C n ( a 1 , … , a k ) is a graph with n vertices { v 0 , … , v n − 1 } such that each vertex v i is adjacent to vertices v ( i + a j ) m o d n , for j = 1 , … , k . In this paper we investigate the vertex colouring problem on circulant graphs. We approach the problem in a purely combinatorial way based on an array representation and propose an exact O ( k 3 log 2 n + n ) algorithm for a subclass of 3-chromatic C n ( a 1 , … , a k ) ’s with k ≥ 2 , which are characterized in the paper. [ABSTRACT FROM AUTHOR]

Many hard graph problems, such as Hamiltonian Cycle, become FPT when parameterized by treewidth, a parameter that is bounded only on sparse graphs. When parameterized by the more general parameter clique-width, Hamiltonian Cycle becomes W[1]-hard, as shown by Fomin et al. (2010). Sæther and Telle address this problem in their paper (Sæther and Telle, 2016) by introducing a new parameter, split-matching-width, which lies between treewidth and clique-width in terms of generality. They show that even though graphs of restricted split-matching-width might be dense, solving problems such as Hamiltonian Cycle can be done in FPT time. Recently, it was shown that Hamiltonian Cycle parameterized by treewidth is in EPT (Bodlaender et al., 2013; Fomin et al., 2014), meaning it can be solved in n O ( 1 ) 2 O ( k ) -time. In this paper, using tools from Fomin et al. (2014), we show that also parameterized by split-matching-width Hamiltonian Cycle is EPT. To the best of our knowledge, this is the first EPT algorithm for any “globally constrained” graph problem parameterized by a non-trivial and non-sparse structural parameter. To accomplish this, we also give an algorithm constructing a branch decomposition approximating the minimum split-matching-width to within a constant factor. Combined, these results show that the algorithms in Sæther and Telle (2016) for Edge Dominating Set, Chromatic Number and Max Cut all can be improved. In fact, using our new approximation algorithm, under the Exponential Time Hypothesis, the Hamiltonian Cycle algorithm of this paper, and the three algorithms for MaxCut, Edge Dominating Set, and Chromatic Number, are asymptotically optimal. [ABSTRACT FROM AUTHOR]

A fast dynamics model that captures the deployment dynamics of self-actuated, origami-inspired, folded planar spacecraft structures is desired for design and verification applications. In this paper, a general simulation framework for numerically generating the equations of motion of any structure that complies with a set of pattern assumptions is presented. The framework is built through application of the articulated body forward dynamics algorithm and the tree-augmented approach for closed-chain forward dynamics. These are multi-body dynamics approaches developed in the literature for complex robotic manipulator systems. Unique adaptations are required to address the highly constrained nature of a folding structure. This solution is desirable due to the computational efficiency of the base algorithms and the ability to analyze multiple systems without reformulation of the core dynamics algorithm. Baumgarte stabilization techniques are applied to address constraint violations, but are found to be a continuing challenge for folding structures with several closed-chains. • Graph theory analysis of benchmark origami fold patterns is presented. • Dynamics algorithms are adapted for origami-folded spacecraft structures. • The approach is demonstrated with multiple numerical cases and constraint challenges are discussed. [ABSTRACT FROM AUTHOR]

In this paper, the Periodic Capacitated Arc Routing Problem (PCARP) is investigated. PCARP is an extension of the well-known CARP from a single period to a multi-period horizon. In PCARP, two objectives are to be minimized. One is the number of required vehicles ( nv ), and the other is the total cost ( tc ). Due to the multi-period nature, given the same graph or road network, PCARP can have a much larger solution space than the single-period CARP counterpart. Furthermore, PCARP consists of an additional allocation sub-problem (of the days to serve the arcs), which is interdependent with the routing sub-problem. Although some attempts have been made for solving PCARP, more investigations are yet to be done to further improve their performance especially on large-scale problem instances. It has been shown that optimizing nv and tc separately (hierarchically) is a good way of dealing with the two objectives. In this paper, we further improve this strategy and propose a new Route Decomposition (RD) operator thereby. Then, the RD operator is integrated into a Memetic Algorithm (MA) framework for PCARP, in which novel crossover and local search operators are designed accordingly. In addition, to improve the search efficiency, a hybridized initialization is employed to generate an initial population consisting of both heuristic and random individuals. The MA with RD (MARD) was evaluated and compared with the state-of-the-art approaches on two benchmark sets of PCARP instances and a large data set which is based on a real-world road network. The experimental results suggest that MARD outperforms the compared state-of-the-art algorithms, and improves most of the best-known solutions. The advantage of MARD becomes more obvious when the problem size increases. Thus, MARD is particularly effective in solving large-scale PCARP instances. Moreover, the efficacy of the proposed RD operator in MARD has been empirically verified. [ABSTRACT FROM AUTHOR]

This paper presents a new algorithmic framework for some basic problems on binary images. Algorithms for binary images such as one of extracting a connected component containing a query pixel and that of connected components labeling play basic roles in image processing. Those algorithms usually use linear work space for efficient implementation. In this paper we propose algorithms for several basic problems on binary images which are efficient in time and space, using space-efficient algorithms for grid graphs. More exactly, some of them run in O ( n log n ) time using O ( 1 ) work space and the others run in O ( n ) or O ( n log n ) time using O ( n ) work space for a binary image of n pixels stored in a read-only array. [ABSTRACT FROM AUTHOR]

The increasing demand for missions involving unmanned aerial vehicles (UAVs) raises the need for reliable and accurate time synchronization in ad hoc networks. Time synchronization plays a crucial role in coordinating the actions of multiple UAVs, particularly when it comes to positioning, coordination, and data fusion. However, achieving high-precision time synchronization is challenging due to the difficult-to-estimate communication transmission delay, measurement noise, relative motion, and clock source characteristics in wireless ad hoc networks formed by UAVs. To address this issue, this paper proposes a fully distributed high-precision network time synchronization algorithm that is suitable for multi-hop dynamic ad hoc networks. The proposed algorithm is based on bidirectional pseudo-range measurements, graph theory, and random matrix correlation theory. It is composed of relative clock skew estimation, logic clock skew compensation and logic clock offset compensation. The algorithm is rigorously derived, requiring no central node, and it is capable of obtaining relative clock skew even when nodes broadcast clock information asynchronously. In addition, the proposed algorithm enables real-time elimination of transmission delays and has noise-resistant capabilities. Simulation results validate the effectiveness of the algorithm, demonstrating that the time synchronization accuracy in UAV ad hoc networks can reach the sub-nanosecond level. [ABSTRACT FROM AUTHOR]

A graph G = ( V , E ) is a word-representable graph if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if ( x , y ) ∈ E for each x ≠ y . In this paper we give an effective characterization of word-representable graphs in terms of orientations. Namely, we show that a graph is word-representable if and only if it admits a semi-transitive orientation defined in the paper. This allows us to prove a number of results about word-representable graphs, in particular showing that the recognition problem is in NP, and that word-representable graphs include all 3-colorable graphs. We also explore bounds on the size of the word representing the graph. The representation number of G is the minimum k such that G is a representable by a word, where each letter occurs k times; such a k exists for any word-representable graph. We show that the representation number of a word-representable graph on n vertices is at most 2 n , while there exist graphs for which it is n / 2 . [ABSTRACT FROM AUTHOR]

This paper introduces the notion of involution module, the first generalization of the modular decomposition of 2-structures which has a unique linear-sized decomposition tree. We derive an O ( n 2 ) decomposition algorithm and we take advantage of the involution modular decomposition tree to obtain several algorithmic results. It is well-known that cographs (or equivalently P 4 -free graphs) are the graphs that are totally decomposable w.r.t modular decomposition. In a similar way, we introduce the class of switch cographs, as the class of graphs that are totally decomposable w.r.t involution modular decomposition. This class generalizes the class of cographs and appears to be exactly the class of (Bull, Gem, Co-Gem, C 5 )-free graphs. We use our new decomposition tool to design three practical algorithms for the maximum cut, vertex cover and vertex separator problems. The complexity of these problems was still unknown for this class of graphs. This paper also improves the complexity of the maximum clique, the maximum independent set, the chromatic number and the maximum clique cover problems by giving efficient algorithms, thanks to the decomposition tree. Eventually, we show that this class of graphs has clique-width at most 4 and that a clique-width expression can be computed in linear time. [ABSTRACT FROM AUTHOR]

Intelligence analysis is a domain characterized by a torrent of streaming data within which a very small portion contains useful knowledge or actionable intelligence. Intelligence analysts have to sift through the compiled data and weave through a complex web of convoluted connections in an attempt to illuminate information requirements (IR) and maintain situational awareness. Automated methodologies have eased the manual burden of this process to some extent. Data are naturally modeled in a graphical form representing the known people, places, events and the relationships between them. Graph matching algorithms in which an information requirement is formulated as a template graph or situation of interest to be found in the observed data graph have been successfully employed in intelligence analysis processes. Absent from these past contributions is the recognition that partial information requirements, such as indicators and warnings, are not mutually exclusive to a specific IR, and an understanding of the characteristics of the underlying data can lead to significant performance benefits. The knowledge of overlapping template sections forms the motivation for precedence tree guided search and AND/OR templates. Through the recognition of the overlapping sections, a single AND/OR template can be created to answer many information requirements. This paper presents a novel algorithm for the intelligent traversal of an AND/OR template, providing increased algorithmic efficiency over the execution of multiple sequential graph matching instances. This paper focuses on development of an algorithm for intelligent AND/OR template traversal with computational results illustrating the effectiveness of the developed methods. The results indicate a significant improvement in runtime (with a speedup over 5 in some cases) while maintaining a good solution quality (within 2% of multiple AND path graph matching executions) in AND/OR and precedence tree guided graph matching. [ABSTRACT FROM AUTHOR]

In this paper, a fault diagnosis (FD) and fault tolerant control (FTC) scheme is proposed for the leader–follower based multiple manipulator system with sensor fault under network communication topology. The learning observer is designed to obtain the fault information when the time-varying sensor fault occurs in follower manipulators. The synchronization error between the leader manipulator and the follower manipulator is defined based on the graph theory. The distributed multiple manipulator synchronization controller is designed for each follower manipulator which contains the value of fault estimation and RBF neural network based approximator. Correspondingly, the stability analysis of the error system is analyzed by the Lyapunov stability theorem. Finally, a simulation example is given to prove the effectiveness of the algorithm. • The learning observer is designed to obtain the sensor fault information. • The manipulator synchronization FTC scheme is designed for the follower manipulator. • The FTC controller can reduce the impact of the sensor fault. [ABSTRACT FROM AUTHOR]

We study the problem of finding in a graph an inclusionwise maximal independent set of minimum cardinality, known as minimum maximal independent set or independent dominating set problem. This is one of the hardest problems in algorithmic graph theory. In particular, restricted to the class of so called SAT-graphs, this problem coincides with satisfiability , the central problem of theoretical computer science. The class of SAT-graphs, and many other important graph classes, such as graphs of bounded vertex degree or line graphs, can be characterized by finitely many forbidden induced subgraphs. We call such classes finitely defined. The paper [R. Boliac and V. Lozin, Independent domination in finitely defined classes of graphs, Theoretical Computer Science, 301 (2003) 271–284] reveals various conditions under which the independent dominating set problem remains NP-hard in a finitely defined class. In the present paper, we identify a number of finitely defined classes where the problem admits polynomial-time solutions. In particular, we prove that the problem is solvable in polynomial time in the class of P 2 + P 3 -free graphs by correcting a mistake of the first two authors of the paper in their earlier solution. This result is in a sharp contrast with the fact that in the class of P 3 + P 3 -free graphs the problem is known to be NP-hard, since this class contains all SAT-graphs. [ABSTRACT FROM AUTHOR]

In this paper, using the properties of graph convergence of H(.,.)-accretive operators, we construct a perturbed algorithm for solving systems of ill-posed variational inclusions involving H(.,.)-accretive operators. Under some suitable conditions, we prove that the sequence generated by the proposed method is strongly convergent to the unique solution of the problem. The main results presented in this paper generalize and improve some recent results in the literature. [ABSTRACT FROM AUTHOR]

Most recent research in graph theory considered the studying of edge regular graph class ER (n,d,λ) for some n > d >λ, such that all the n vertices have d adjacent neighbors, and each pair of adjacent vertices have λ common neighbors, none of these research gave an algorithm to generate this class with considering the λ, in this paper, a novel algorithm to generate random edge-regular graphs for λ > 0. The algorithm produces an edge-regular graph for different values of d and n Moreover, it is easy to implement and quite fast in practice. The Matlab programming language used to obtain the experimental result. The analysis of this method showed that the running time of this method proven to be O( d 3). [ABSTRACT FROM AUTHOR]

Abstract: In this paper 1 [1] The extended abstract of this paper appeared on PPAM 2009, LNCS 6067 (2010) 11–20. we study the problem of interval incidence coloring of bipartite graphs. We show the upper bound for interval incidence coloring number ( ) for bipartite graphs , and we prove that holds for regular bipartite graphs. We solve this problem for subcubic bipartite graphs, i.e. we fully characterize the subcubic graphs that admit 4, 5 or 6 coloring, and we construct a linear time exact algorithm for subcubic bipartite graphs. We also study the problem for bipartite graphs with and we show that 5-coloring is easy and 6-coloring is hard ( -complete). Moreover, we construct an time optimal algorithm for trees. [Copyright &y& Elsevier]

Abstract: Case-Based reasoning (CBR) applications are increasingly used for problems involving structured data, especially in process-oriented domains. Available CBR frameworks rely primarily on flat case representations, leaving developers of process-oriented CBR systems without general-purpose tools aimed at their needs. This paper discusses needs to support structure-based retrieval for CBR and how they have been addressed in the development of the Structure Access Interface (SAI), a toolkit for representation and retrieval of structured cases which is now available for general use. Integrating SAI into a CBR project eliminates the need for developing a storage scheme for graph data structures and facilitates the development of retrieval algorithms by (1) providing useful code for common retrieval tasks and (2) delineating the tasks which may require domain-specific implementations. SAI maintains flexibility through its customizability yet carries solutions for many common tasks for CBR developers, as well as illuminating some general principles for addressing common representation and retrieval needs for process-oriented CBR tasks and the relationship between CBR needs for structured retrieval and needs and methods in graph oriented database research. The paper closes with an evaluation of SAI's scalability and demonstration of the value of enabling developers to select retrieval methods suited to their tasks. It closes with a discussion of SAI's relationship to the growing body of work on graph databases. [Copyright &y& Elsevier]

Abstract: This paper studies a variation of domination in graphs called rainbow domination. For a positive integer , a -rainbow dominating function of a graph is a function such that for any vertex with . The -rainbow domination number of is the minimum value of , where runs over all -rainbow dominating functions of . A related concept is as follows. A weak -dominating function of is a function such that for any vertex with . The weak -domination number of is the minimum value of , where runs over all weak -dominating functions of . In this paper, we prove that for any strongly chordal graph . Our approach is a more general setting called the -function, which leads to interesting results on other variations of domination. We also give a linear-time algorithm for finding the weak -domination numbers of block graphs. [Copyright &y& Elsevier]

Abstract: Let and be fixed positive integers. Assume that the vertices of a planar graph are partitioned into blocks (or empires) each containing exactly vertices. The -colouring problem (- COL r ) asks for a colouring of the vertices of the graph that uses at most colours, never assigns the same colour to adjacent vertices in different empires and, conversely, assigns the same colour to all vertices in the same empire, disregarding adjacencies. For the problem coincides with the classical vertex colouring problem on planar graphs. The generalization for was defined by Percy Heawood in 1890 in the same paper in which he refuted a previous “proof” of the famous Four Colour Theorem. In a recent paper we have shown that if , - COL r is NP-hard for linear forests if . Furthermore, the hardness extends to (resp. ) when (resp. for ) for arbitrary planar graphs. For trees, our argument entails a nice dichotomy: - COL r is NP-hard for and solvable in polynomial time for any other positive value of . In this paper we argue that linear forests do not make the problem any easier, even for small values of . We prove that the - COL r problem is NP-hard for linear forests even if and , or and . [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: Building the behaviour for non-player characters in a game is a complex collaborative task among AI designers and programmers. In this paper we present a visual authoring tool for game designers that supports behaviour reuse. We describe a visual editor, capable of storing, indexing, retrieving and reusing behaviours previously designed by AI programmers. One of the most notable features of our editor is its capability for sketch-based retrieval: searching in a repository for behaviours that are similar to the one the user is drawing, and making suggestions about how to complete it. As this process relies on graph behaviour comparison, in this paper, we describe different algorithms for graph comparison, and demonstrate, through empirical evaluation in a particular test domain, that we can provide structure-based similarity for graphs that preserves behaviour similarity and can be computed at reasonable cost. [Copyright &y& Elsevier]

Abstract: In recent years, the use of extensible processors has been increased. Extensible processors extend the base instruction set of a general-purpose processor with a set of custom instructions. Custom instructions that can be implemented in special hardware units make it possible to improve performance and decrease power consumption in extensible processors. The key issue involved is to generate and select automatically the custom instructions from a high-level application code. In this paper, we propose a new efficient algorithm for the automatic generation of all candidate instructions (or patterns). Our pattern generation algorithm identify all feasible connected and disjoint patterns under different constraints. Compared to a previously proposed well-known algorithm, our algorithm solves the problem more efficiently by taking advantage of the topological property of data flow graph (DFG) as well as overcoming the drawbacks of the previously proposed algorithm. An extension of the proposed algorithm is also presented in this paper. The extended algorithm further radically reduce the search space by considering the input resolving nodes. Experimental results show that our algorithms can achieve orders of magnitude speedup over the well-know algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, a novel image registration method is proposed to achieve accurate registration between images having large shape differences with the help of a set of appropriate intermediate templates. We first demonstrate that directionality is a key factor in both pairwise image registration and groupwise registration, which is defined in this paper to describe the influence of the registration direction and paths on the registration performance. In our solution, the intermediate template selection and intermediate template guided registration are two coherent steps with directionality being considered. To take advantage of the directionality, a directed graph is built based on the asymmetric distance defined on all ordered image pairs in the image population, which is fundamentally different from the undirected graph with symmetric distance metrics in all previous methods, and the shortest distance between template and subject on the directed graph is calculated. The allocated directed path can be thus utilized to better guide the registration by successively registering the subject through the intermediate templates one by one on the path towards the template. The proposed directed graph based solution can also be used in groupwise registration. Specifically, by building a minimum spanning arborescence (MSA) on the directed graph, the population center, i.e., a selected template, as well as the directed registration paths from all the rest of images to the population center, is determined simultaneously. The performance of directed graph based registration algorithm is demonstrated by the spatial normalization on both synthetic dataset and real brain MR images. It is shown that our method can achieve more accurate registration results than both the undirected graph based solution and the direct pairwise registration. [Copyright &y& Elsevier]

Adaptive modification design occupies a large proportion in modern product design, which is essentially a coordination process. Due to the conduction phenomenon, it often leads to the problem that the solution space is too large or even unsolvable. Aiming at the problems caused by the conduction phenomenon, an optimal coordination path selecting method for conduction transformation based Floyd algorithm is proposed. The product conduction transformation coordination process is considered as a path by combining the product graph theory model. The selection criteria of the start and end nodes is given. The functional contribution index, modified adaptation index and conduction impact index are described in detail. The calculation of the comprehensive coordination factor composed of them is given and used as the evaluation index of the conduction transformation coordination path. Floyd algorithm is adopted to coordination path optimization selection model, case study and system development, in order to verify the method proposed in this paper. [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]

Abstract The Internet of Things (IoT) contains a diverse set of sensors, actuators and other Internet-connected devices communicating, processing data and performing a multitude of functions. It is emerging as an integral part of societal infrastructure enabling smart services. However, these connected objects might have various vulnerabilities that can lead to serious security compromises and breaches. Securing and hardening of IoT systems is thus of vital importance. In that regard, attack graphs provide analytical support to prevent multistep network attacks by showing all possible sequences of vulnerabilities and their interactions. Since attack graphs generally consist of a very large number of nodes, it is computationally challenging to analyze them for network hardening. In this paper, we propose a greedy algorithm using compact attack graphs to find a cost-effective solution to protect IoT systems. First, we extract all possible attack paths which reach predetermined critical resources embedded in the network. Then, exploit or initial condition with minimum effective cost is selected to be removed. This cost is calculated as a function of contribution to attack paths (the higher, the better) and removal cost (the lower, the better). This process continues iteratively until the total cost exceeds the allocated budget. The experimental results show that our algorithm scales almost linearly with the network size and it can be applied to large-scale graphs with a very large number of IoT nodes. In addition to network-hardening, our proposal measures the security level of the network in every step to demonstrate the vulnerability grade of the system. [ABSTRACT FROM AUTHOR]

Abstract An edge metric generator of a connected graph G is a vertex subset S for which every two distinct edges of G have distinct distance to some vertex of S , where the distance between a vertex v and an edge e is defined as the minimum of distances between v and the two endpoints of e in G. The smallest cardinality of an edge metric generator of G is the edge metric dimension, denoted by dim e (G). It follows that 1 ≤ dim e (G) ≤ n − 1 for any n -vertex graph G. A graph whose edge metric dimension achieves the upper bound is topful. In this paper, the structure of topful graphs is characterized, and many necessary and sufficient conditions for a graph to be topful are obtained. Using these results we design an O (n 3) time algorithm which determines whether a graph of order n is topful or not. Moreover, we describe and address an interesting class of topful graphs whose super graphs obtained by adding one edge are not topful. [ABSTRACT FROM AUTHOR]

Abstract: Nowadays SAT algorithms allow larger problem instances to be solved in application domains such as automatic test pattern generation (ATPG) that can also be viewed as solving a SAT problem. The key to a SAT-solver can be scalable is that it is able to take into account the information of high-level structure of formulas. This paper further improves to SAT-based ATPG by analyzing specific structure of circuit instances. This analysis is called heuristic learning where correlations among signals have been established by simple and efficient methods. It is achieved by finding more necessary signal line assignments, by detecting conflicts earlier, and by avoiding unnecessary work during test generation. Among others things, it combines strengths of binary decision graphs (BDD) and SAT techniques to improve the efficiency of test generation. Reconvergent fanout is a fundamental cause of the difficulty in testing circuits, because they introduce dependencies in the values that can be assigned to nodes. This paper exploits reconvergent fanout analysis of circuit to gather information about local signal correlation through BDD learning, and then used the learned information in the conjunctive normal form clauses to restrict and focus the overall search space of test pattern generation. The experimental results demonstrate the effectiveness of these learning techniques. [Copyright &y& Elsevier]

Abstract: This paper, the third one in a three-paper sequence, presents the result of TOSSIM simulation of a Hopfield neural network as a static optimizer and configured to solve the maximum independent set (MIS) problem using a wireless sensor network as a fully parallel and distributed computing hardware platform. TinyOS with its default protocol stack along with nesC were used to develop the simulation model. Simulations were realized for mote counts of 10, 50, 100, and 182; messaging complexity, memory and simulation time costs were measured. Results indicated, as the most prominent finding, that the neural optimization algorithm was able to compute solutions to the MIS problem. The memory footprint of the TOSSIM process in Windows XP environment was about 20 MB for the range of sensor networks considered. The messaging complexity as measured by the total number of messages transmitted and the simulation time increased rather quickly indicating a need to optimize and tune certain aspects of the simulation environment if wireless sensor networks with higher mote counts need to be simulated. [Copyright &y& Elsevier]

Abstract: Finding the lowest common ancestor (LCA) of two nodes in a binary tree has been focused both in graph theory and computer science. The paper puts forward and proves an analytic criterion for the LCA of two neighboring nodes in a complete binary tree. The criterion mainly concerns addition, subtraction and bitwise operations, needs no searching procedures and thus is easy to implement in software programming as well as hardware programming. An algorithm that has logarithmic time complexity is also presented with C-language implementation in the paper. [Copyright &y& Elsevier]

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: A project is an enterprise consisting of several activities which are to be carried out in some specific order. The activities and the order in which they need to be carried out can be represented by a PERT network. The PERT technique is a traditional, well-known approach to the expert of project management. When networks are used, it often becomes necessary to draw dummy activities. Since the computation of project completion time is proportional to the number of arcs, including dummy arcs, it is desirable to draw a network with as few dummy activities as possible. In this paper, we propose a new method for constructing, for a given project scheduling problem, a PERT network having as small as possible the number of dummy arcs by using some results on line graphs. This algorithm deals with the existence of transitive arcs. The paper contains illustrative examples, proofs of some theoretical results as well as a comparative study with a similar algorithm known in the literature. Computational results showed the superiority of our algorithm. [Copyright &y& Elsevier]

Abstract: Automatic program generation is one of the applicable fields of evolutionary computation, and Genetic Programming (GP) is the typical method for this field. On the other hand, Genetic Network Programming (GNP) has been proposed as an extended algorithm of GP in terms of gene structures. GNP is a graph-based evolutionary algorithm and applied to automatic program generation in this paper. GNP has directed graph structures which have some features inherently, for example, re-usability of nodes and the small number of nodes. These features contribute to creating complicated programs with compact structures and never cause bloat. In this paper, the extended algorithm of GNP is proposed, which can create plural programs simultaneously in one individual by using multi-start nodes. In addition, GNP can evolve the programs in one individual considering the fitness and also its standard deviation in order to evolve the plural programs efficiently. In the simulations, Even-n-Parity problem and Mirror Symmetry problem are used for the performance evaluation, and the results show that the proposed method outperforms the standard GNP with single start node. [Copyright &y& Elsevier]

Abstract: A (weak) closed rectangle-of-influence (RI for short) drawing is a straight-line planar grid drawing in which there is no other vertex inside or on the boundary of the axis parallel rectangle defined by the two end vertices of any edge. Biedl et al. (1999) showed that a plane graph G has a closed RI drawing, if and only if it has no filled 3-cycle (a cycle of 3 vertices such that there is a vertex in the proper interior). They also showed that such a graph G has a closed RI drawing in an grid, where n is the number of vertices in G. They raised an open question on whether this grid size bound can be improved (Biedl et al., 1999 ). Without loss of generality, we investigate maximal plane graphs admitting closed RI drawings in this paper. They are plane graphs with a quadrangular exterior face, triangular interior faces and no filled 3-cycles, known as irreducible triangulations (Fusy, 2009 ). In this paper, we present a linear time algorithm that computes closed RI drawings for irreducible triangulations. Given an arbitrary irreducible triangulation G with n vertices, our algorithm produces a closed RI drawing with size at most ; and for a random irreducible triangulation, the expected grid size of the drawing is . We then prove that for arbitrary , there is an n-vertex irreducible triangulation, such that any of its closed RI drawing requires a grid of size . Thus the grid size of the drawing produced by our algorithm is tight. This lower bound also answers the open question posed in Biedl et al. (1999) negatively. [ABSTRACT FROM AUTHOR]

Abstract Several graph theoretic watermark methods have been proposed to encode numbers as graph structures in software watermarking environments. In this paper we propose an efficient and easily implementable codec system for encoding watermark numbers as reducible permutation flow-graphs and, thus, we extend the class of graphs used in such a watermarking environment. More precisely, we present an algorithm for encoding a watermark number w as a self-inverting permutation π ∗ , an algorithm for encoding the self-inverting permutation π ∗ into a reducible permutation graph F [ π ∗ ] whose structure resembles the structure of real program graphs, as well as decoding algorithms which extract the permutation π ∗ from the reducible permutation graph F [ π ∗ ] and the number w from π ∗. Both the encoding and the decoding process take, in the worst-case, time and space linear in the length of the binary representation of w. The two main components of our proposed codec system, i.e., the self-inverting permutation π ∗ and the reducible permutation graph F [ π ∗ ] , incorporate the binary representation of the watermark w in their structure and possess important structural properties, which make our system resilient to attacks; to this end, we experimentally evaluated our system under edge modification attacks on the graph F [ π ∗ ] and the results suggest that we can detect such attacks with high probability. [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 Containing many classic optimization problems, the family of vertex deletion problems has an important position in algorithm and complexity study. The celebrated result of Lewis and Yannakakis gives a complete dichotomy of their complexity. It however has nothing to say about the case when the input graph is also special. This paper initiates a systematic study of vertex deletion problems from one subclass of chordal graphs to another. We give polynomial-time algorithms or proofs of NP-completeness for most of the problems. In particular, we show that the vertex deletion problem from chordal graphs to interval graphs is NP-complete. [ABSTRACT FROM AUTHOR]

Abstract Given a graph G and a pair of vertices u , v the interval I G [ u , v ] is the set of all vertices that are in some shortest path between u and v. Given a subset X of vertices of G , the interval I G [ X ] of X , is the union of the intervals for all pairs of vertices in X and we say that X is geodetic if its interval do coincide with the set of vertices in the graph. A minimum geodetic set is a minimum cardinality geodetic set of G. The problem of computing a minimum geodetic set is known to be NP-Hard for general graphs but is known to be polynomially solvable for maximal outerplanar graphs. In this paper we show a polynomial time algorithm for finding a minimum geodetic set in general outerplanar graphs. [ABSTRACT FROM AUTHOR]

A graph is equimatchable if all of its maximal matchings have the same size. A graph is claw-free if it does not have a claw as an induced subgraph. In this paper, we provide the first characterization of claw-free equimatchable graphs by identifying the equimatchable claw-free graph families. This characterization implies an efficient recognition algorithm. [ABSTRACT FROM AUTHOR]

Given a graph G = ( V , E ) of order n and maximum degree Δ , the NP -complete S - labeling problem consists in finding a labeling of G , i.e. a bijective mapping ϕ : V → { 1 , 2 … n } , such that SL ϕ ( G ) = ∑ u v ∈ E min { ϕ ( u ) , ϕ ( v ) } is minimized. In this paper, we study the S - labeling problem, with a particular focus on algorithmic issues. We first give intrinsic properties of optimal labelings, which will prove useful for our algorithmic study. We then provide lower bounds on SL ϕ ( G ) , together with a generic greedy algorithm, which collectively allow us to approximate the problem in several classes of graphs—in particular, we obtain constant approximation ratios for regular graphs and bounded degree graphs. We also show that deciding whether there exists a labeling ϕ of G such that SL ϕ ( G ) ≤ | E | + k is solvable in O ∗ ( 2 2 k ( 2 k ) ! ) time, thus fixed-parameterized tractable in k . We finally show that the S - Labeling problem is polynomial-time solvable for two classes of graphs, namely split graphs and (sets of) caterpillars. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with problems on non-oriented edge-colored graphs. The aim is to find a route between two given vertices and . This route can be a walk, a trail or a path. Each time a vertex is crossed by a walk there is an associated non-negative reload cost , where and denote, respectively, the colors of successive edges in this walk. The goal is to find a route whose total reload cost is minimum. Polynomial algorithms and proofs of NP-hardness are given for particular cases: when the triangle inequality is satisfied or not, when reload costs are symmetric (i.e., ) or asymmetric. We also investigate bounded degree graphs and planar graphs. We conclude the paper with the traveling salesman problem with reload costs. [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: This paper introduces a novel approach to the task of lexical translation between languages for which no translation dictionaries are available. We build a massive translation graph, automatically constructed from over 630 machine-readable dictionaries and Wiktionaries. In this graph each node denotes a word in some language and each edge denotes a word sense shared by and . Our current graph contains over 10,000,000 nodes and expresses more than 60,000,000 pairwise translations. The composition of multiple translation dictionaries leads to a transitive inference problem: if word A translates to word B which in turn translates to word C, what is the probability that C is a translation of A? The paper describes a series of probabilistic inference algorithms that solve this problem at varying precision and recall levels. All algorithms enable us to quantify our confidence in a translation derived from the graph, and thus trade precision for recall. We compile the results of our best inference algorithm to yield PanDictionary, a novel multilingual dictionary. PanDictionary contains more than four times as many translations as in the largest Wiktionary at precision 0.90 and over 200,000,000 pairwise translations in over 200,000 language pairs at precision 0.8. [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 the evacuation problem in a network which consists of a directed graph with capacities and transit times on its arcs. This problem can be solved by the algorithm of Hoppe and Tardos [B. Hoppe, É. Tardos, The quickest transshipment problem, Math. Oper. Res. 25(1) (2000) 36–62] in polynomial time. However their running time is high-order polynomial, and hence is not practical in general. Thus, it is necessary to devise a faster algorithm for a tractable and practically useful subclass of this problem. In this paper, we consider a network with a sink such that (i) for each vertex the sum of the transit times of arcs on any path from to takes the same value, and (ii) for each vertex the minimum - cut is determined by the arcs incident to whose tails are reachable from . This class of networks is a generalization of grid networks studied in the paper [N. Kamiyama, N. Katoh, A. Takizawa, An efficient algorithm for evacuation problem in dynamic network flows with uniform arc capacity, IEICE Trans. Infrom. Syst. E89-D (8) (2006) 2372–2379]. We propose an efficient algorithm for this network problem. [Copyright &y& Elsevier]