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The problem of finding a maximum size matching in a graph (known as the maximum matching problem) is one of the most classical problems in computer science. Despite a significant body of work dedicated to the study of this problem in the data stream model, the state-of-the-art single-pass semi-streaming algorithm for it is still a simple greedy algorithm that computes a maximal matching, and this way obtains 1 / 2 -approximation. Some previous works described two/three-pass algorithms that improve over this approximation ratio by using their second and third passes to improve the above mentioned maximal matching. One contribution of this paper continues this line of work by presenting new three-pass semi-streaming algorithms that work along these lines and obtain improved approximation ratios of 0.6111 and 0.5694 for triangle-free and general graphs, respectively. Unfortunately, a recent work Konrad and Naidu (Approximation, randomization, and combinatorial optimization. Algorithms and techniques, APPROX/RANDOM 2021, August 16–18, 2021. LIPIcs, vol 207, pp 19:1–19:18, 2021. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.19) shows that the strategy of constructing a maximal matching in the first pass and then improving it in further passes has limitations. Additionally, this technique is unlikely to get us closer to single-pass semi-streaming algorithms obtaining a better than 1 / 2 -approximation. Therefore, it is interesting to come up with algorithms that do something else with their first pass (we term such algorithms non-maximal-matching-first algorithms). No such algorithms were previously known, and the main contribution of this paper is describing such algorithms that obtain approximation ratios of 0.5384 and 0.5555 in two and three passes, respectively, for general graphs. The main significance of our results is not in the numerical improvements, but in demonstrating the potential of non-maximal-matching-first algorithms. [ABSTRACT FROM AUTHOR]

We consider the weighted k-set packing problem, where, given a collection S of sets, each of cardinality at most k, and a positive weight function w : S → Q > 0 , the task is to find a sub-collection of S consisting of pairwise disjoint sets of maximum total weight. As this problem does not permit a polynomial-time o (k log k) -approximation unless P = N P (Hazan et al. in Comput Complex 15:20–39, 2006. https://doi.org/10.1007/s00037-006-0205-6), most previous approaches rely on local search. For twenty years, Berman's algorithm SquareImp (Berman, in: Scandinavian workshop on algorithm theory, Springer, 2000. https://doi.org/10.1007/3-540-44985-X%5f19), which yields a polynomial-time k + 1 2 + ϵ -approximation for any fixed ϵ > 0 , has remained unchallenged. Only recently, it could be improved to k + 1 2 - 1 63 , 700 , 993 by Neuwohner (38th International symposium on theoretical aspects of computer science (STACS 2021), Leibniz international proceedings in informatics (LIPIcs), 2021. https://doi.org/10.4230/LIPIcs.STACS.2021.53). In her paper, she showed that instances for which the analysis of SquareImp is almost tight are "close to unweighted" in a certain sense. But for the unit weight variant, the best known approximation guarantee is k + 1 3 + ϵ (Fürer and Yu in International symposium on combinatorial optimization, Springer, 2014. https://doi.org/10.1007/978-3-319-09174-7%5f35). Using this observation as a starting point, we conduct a more in-depth analysis of close-to-tight instances of SquareImp. This finally allows us to generalize techniques used in the unweighted case to the weighted setting. In doing so, we obtain approximation guarantees of k + ϵ k 2 , where lim k → ∞ ϵ k = 0 . On the other hand, we prove that this is asymptotically best possible in that local improvements of logarithmically bounded size cannot produce an approximation ratio below k 2 . [ABSTRACT FROM AUTHOR]

The vertex coloring problem is a classical problem in combinatorial optimization that consists of assigning a color to each vertex of a graph such that no adjacent vertices share the same color, minimizing the number of colors used. Despite the various practical applications that exist for this problem, its NP-hardness still represents a computational challenge. Some of the best computational results obtained for this problem are consequences of hybridizing the various known heuristics. Automatically revising the space constituted by combining these techniques to find the most adequate combination has received less attention. In this paper, we propose exploring the heuristics space for the vertex coloring problem using evolutionary algorithms. We automatically generate three new algorithms by combining elementary heuristics. To evaluate the new algorithms, a computational experiment was performed that allowed comparing them numerically with existing heuristics. The obtained algorithms present an average 29.97% relative error, while four other heuristics selected from the literature present a 59.73% error, considering 29 of the more difficult instances in the DIMACS benchmark. [ABSTRACT FROM AUTHOR]

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]

Detection of copositivity plays an important role in combinatorial and quadratic optimization. Recently, an algorithm for copositivity detection by simplicial partition has been proposed. In this paper, we develop an improved depth-first simplicial partition algorithm which reduces memory requirements significantly and therefore enables copositivity checks of much larger matrices - of size up to a few thousands instead of a few hundreds. The algorithm has been investigated experimentally on a number of MaxClique problems as well as on generated random problems. We present numerical results showing that the algorithm is much faster than a recently published linear algebraic algorithm for copositivity detection based on traditional ideas - checking properties of principal sub-matrices. We also show that the algorithm works very well for solving MaxClique problems through copositivity checks. [ABSTRACT FROM AUTHOR]

A polygonal approximation captures the essential features of a digital planar curve and yields a compact representation. Those points of the digital curve that carry vital information about the shape of the curve form the vertices of the approximating polygon and are called significant vertices. In this paper, we present a genetic algorithm-based approach to locate a specified number of significant points, such that the approximation error between the original curve and its polygonal version obtained by joining the adjacent significant points is minimized. By using a priori knowledge about the shape of the curve we confine our search to only those points of the curve that have the potential of qualifying as significant points. We also incorporate chromosome differentiation to improve upon the effectiveness of the search in arriving at a near-optimal polygonal approximation. Finally, we show that the proposed method performs remarkably well when evaluated in terms of the metrics available for assessing the goodness of a polygonal approximation algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we present an approach for writer identification carried out using off-line Arabic handwriting. Our proposed method is based on the combination of global and structural features. We used genetic algorithm for feature subset selection in order to eliminate the redundant and irrelevant ones. A comparative evaluation between two classifiers is done using Support Vector Machines and Multilayer Perceptron (MLP). The best results have been achieved using optimal feature subset and MLP with an average rate of 94%. Experiments have been carried out on a database of 120 text samples. The choice of the text samples was made to ensure the involvement of the various internal shapes and letter locations within a subword. [ABSTRACT FROM AUTHOR]

Abstract: Trade-off (aka Pareto) curves are typically used to represent the trade-off among different objectives in multiobjective optimization problems. Although trade-off curves are exponentially large for typical combinatorial optimization problems (and infinite for continuous problems), it was observed in Papadimitriou and Yannakakis [On the approximability of trade-offs and optimal access of web sources, in: Proc. 41st IEEE Symp. on Foundations of Computer Science, 2000] that there exist polynomial size approximations for any , and that under certain general conditions, such approximate -Pareto curves can be constructed in polynomial time. In this paper we seek general-purpose algorithms for the efficient approximation of trade-off curves using as few points as possible. In the case of two objectives, we present a general algorithm that efficiently computes an -Pareto curve that uses at most 3 times the number of points of the smallest such curve; we show that no algorithm can be better than 3-competitive in this setting. If we relax to any , then we can efficiently construct an -curve that uses no more points than the smallest -curve. With three objectives we show that no algorithm can be c-competitive for any constant c unless it is allowed to use a larger value. We present an algorithm that is 4-competitive for any . We explore the problem in high dimensions and give hardness proofs showing that (unless P=NP) no constant approximation factor can be achieved efficiently even if we relax by an arbitrary constant. [Copyright &y& Elsevier]

The cerebellar model arithmetic computer (CMAC) is a kind of neural network that is capable of high-speed learning. In the use of the CMAC, various parameters must be defined, but it is difficult to set the parameters adequately. The pseudo-bacterial genetic algorithm (PBGA) is a kind of evolutionary computation which offers local search. This paper considers adequate determination of the location of the boundary line, which is one of the parameters of the CMAC. For that purpose the PBGA is applied, and PBGA/CMAC, which realizes the efficient search of the boundary line of the CMAC, is proposed. Furthermore, since PBGA/CMAC requires a large amount of computation, a hardware implementation is considered in order to improve the computation speed. The computation involved in the learning rules of the CMAC is divided into four stages, and the structure is implemented as a pipeline. The pipeline implementation produces read-after-write hazards for the granular cell values. However, it is shown that the difference in performance from conventional CMAC learning rule is small, indicating the possibility of achieving high-speed learning. The speed of PBGA/CMAC hardware is improved to 140 times the speed of operation by software. In order to present a guide for PBGA/CMAC hardware, the hardware volume is evaluated, and it is shown that it can be implemented with precision sufficient for practice. © 2004 Wiley Periodicals, Inc. Syst Comp Jpn, 35(11): 14–23, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10437 [ABSTRACT FROM AUTHOR]

In this paper we present a version of genetic algorithm (GA) where parameters are created by the GA, rather than predetermined by the programmer. Chromosome portions which do not translate into fitness ("genetic residual") are given function to diversify control parameters for the GA, providing random parameter setting along the way, and doing away with fine-tuning of probabilities of crossover and mutation. We test the algorithm on Royal Road functions to examine the difference between our version (GAR) and the simple genetic algorithm (SGA) in the speed of discovering schema and creating building blocks. We also look at the usefulness of other standard improvements, such as non-coding segments, elitist selection and multiple crossover on the evolution of schema. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel analog neural approach to combinatorial optimization problems, in particular, the quadratic assignment problem (QAP). Our proposed method is based on an analog version of the λ-opt heuristics, which simultaneously changes assignments for λ elements in a permutation. Since we can take a relatively large λ value, our method can achieve a middle-range search over the possible solutions, and this helps the system neglect shallow local minima and escape from local minima. In experiments, we have applied our method to relatively large-scale (N = 80 to 150) QAPs. Results have shown that our new method is comparable to the present champion algorithms, and for two benchmark problems, it is able to obtain better solutions than the previous champion algorithms. © 2000 Scripta Technica, Syst Comp Jpn, 31(10): 1–9, 2000 [ABSTRACT FROM AUTHOR]

There are two main points in this paper. First, the tree structure was mounted on the chromosome structure of a simple GA. Next, this method succeeded in identifying functions. The target functions for identification were composed of algebraic functions, primary transcendental functions, time series functions, and user-defined one-variable functions. The experimental results indicate that identification of expanded functions succeeded at high speed. However, functions were not identified in factorized form. A second solution method is proposed and experimental results described. © 2000 Scripta Technica, Syst Comp Jpn, 31(10): 32–40, 2000 [ABSTRACT FROM AUTHOR]

Travelling Salesman problem is a nondeterministic polynomial time hard problem in combinatorial optimization studied in operational research and theoretical computer science. In this review paper several techniques like brute-force method, nearest neighbour, branch and bound, dijkstra shortest path algorithm, bellman ford, Floyd warshall algorithm and some heuristic techniques like ant colony optimization and genetic algorithm used to solve the travelling salesman problem are analysed. The comparison between these techniques is accomplished to state which is the better one for solving travelling salesman problem. [ABSTRACT FROM AUTHOR]

The detection of evolving communities in dynamic complex networks is a challenging problem that recently received attention from the research community. Dynamics clearly add another complexity dimension to the difficult task of community detection. Methods should be able to detect changes in the network structure and produce a set of community structures corresponding to different timestamps and reflecting the evolution in time of network data. We propose a novel approach based on game theory elements and extremal optimization to address dynamic communities detection. Thus, the problem is formulated as a mathematical game in which nodes take the role of players that seek to choose a community that maximizes their profit viewed as a fitness function. Numerical results obtained for both synthetic and real-world networks illustrate the competitive performance of this game theoretical approach. [ABSTRACT FROM AUTHOR]

Modern algorithm theory includes numerous techniques to attack hard problems, such as approximation algorithms on the one hand and parameterized complexity on the other hand. However, it is still uncommon to use these two techniques simultaneously, which is unfortunate, as there are natural problems that cannot be solved using either technique alone, but rather well if we combine them. The problem to be studied here is not only natural, but also practical: Consider TSP, generalized as follows. We impose deadlines on some of the vertices, effectively constraining them to be visited prior to a given point of time. The resulting problem DlTSP (a special case of the well-known TSP with time windows) inherits its hardness from classical TSP, which is both well known from practice and renowned to be one of the hardest problems with respect to approximability: Within polynomial time, not even a polynomial approximation ratio (let alone a constant one) can be achieved (unless P = NP). We will show that DlTSP is even harder than classical TSP in the following sense. Classical TSP, despite its hardness, admits good approximation algorithms if restricted to metric (or near-metric) inputs. Not so DlTSP (and hence, neither TSP with time windows): We will prove that even for metric inputs, no constant approximation ratio can ever be achieved (unless P = NP). This is where parameterization becomes crucial: By combining methods from the field of approximation algorithms with ideas from the theory of parameterized complexity, we apply the concept of parameterized approximation. Thereby, we obtain a 2.5-approximation algorithm for DlTSP with a running time of k! · poly(|G|), where k denotes the number of deadlines. Furthermore, we prove that there is no fpt-algorithm with an approximation guarantee of 2-ε for any ε > 0, unless P = NP. Finally, we show that, unlike TSP, DlTSP becomes much harder when relaxing the triangle inequality. More precisely, for an arbitrary small violation of the triangle inequality, DlTSP does not admit an fpt-algorithm with approximation guarantee ((1-ε)/2)|V| for any ε > 0, unless P = NP. [ABSTRACT FROM AUTHOR]

It is not an easy task to know a priori the most appropriate fuzzy sets that cover the domains of quantitative attributes for fuzzy association rules mining. In general, it is unrealistic that experts can always provide such sets. And finding the most appropriate fuzzy sets becomes a more complex problem when items are not considered to have equal importance and the support and confidence parameters required for the association rules mining process are specified as linguistic terms. Existing clustering based automated methods are not satisfactory because they do not consider the optimization of the discovered membership functions. In order to tackle this problem, we propose Genetic Algorithms (GAs) based clustering method, which dynamically adjusts the fuzzy sets to provide maximum profit based on user specified linguistic minimum support and confidence terms. This is achieved by tuning the base values of the membership functions for each quantitative attribute with respect to two different evaluation functions maximizing the number of large itemsets and the average of the confidence intervals of the generated rules. To the best of our knowledge, this is the first effort in this direction. Experiments conducted on 100 K transactions from the adult database of United States census in year 2000 demonstrate that the proposed clustering method exhibits good performance in terms of the number of produced large itemsets and interesting association rules. [ABSTRACT FROM AUTHOR]

The knapsack problem and the minimum spanning tree problem are both fundamental in operations research and computer science. We are concerned with a combination of these two problems. That is, we are given a knapsack of a fixed capacity, as well as an undirected graph where each edge is associated with profit and weight. The problem is to fill the knapsack with a feasible spanning tree such that the tree profit is maximized. We prove this problem 𝒩𝒫-hard, present upper and lower bounds, develop a branch-and-bound algorithm to solve the problem to optimality and propose a shooting method to accelerate computation. We evaluate the developed algorithm through a series of numerical experiments for various types of test problems. [ABSTRACT FROM AUTHOR]