Computational and storage costs of resolution of large sparse linear systems Ax = b can be performed by reducing the bandwidth of A. Bandwidth reduction consists of carrying out permutations of lines and columns so th...
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Computational and storage costs of resolution of large sparse linear systems Ax = b can be performed by reducing the bandwidth of A. Bandwidth reduction consists of carrying out permutations of lines and columns so that they allow coefficients to remain near the main diagonal. When considering an adjacency matrix of a graph, bandwidth reduction can be considered in the sense of modifying the order in which the graph vertices are numbered. Heuristics for bandwidth reduction are revised in this study, aiming at determining which of them offers the higher bandwidth reduction with a reasonable computational cost. Specifically, metaheuristic-based heuristics are reviewed in this systematic review. Moreover, 29 metaheuristic-based heuristics tested for bandwidth reduction were found. Among them, 4 are recommended as possible state-of-the-art heuristics for addressing the problem.
This paper concentrates on low-cost heuristics for profile reduction. Low-cost methods for profile reduction are mainly heuristic in nature and based on graph-theoretic concepts. The contribution of this paper is twof...
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ISBN:
(纸本)9783030242893
This paper concentrates on low-cost heuristics for profile reduction. Low-cost methods for profile reduction are mainly heuristic in nature and based on graph-theoretic concepts. The contribution of this paper is twofold. Firstly, the paper includes a section involving a numerical examination of the current state-of-art metaheuristic and graph-theoretic methods for matrix profile reduction. With the support of extensive experiments, this paper shows that the metaheuristic-based algorithm is capable of reducing the profile of some matrices where the other algorithms do not perform well, but on average, the profile reduction obtained is similar for these algorithms, whereas the metaheuristicbased algorithm takes seven orders of magnitude more running time. These high execution times make the metaheuristic-based algorithm a noncontender for sparse matrix factorization and related problems. Secondly, this paper experimentally evaluates a hybrid algorithm based on the MPG and NSloan heuristics. This paper also evaluates the new hybrid heuristic for profile reduction when applied to matrices arising from two application areas against the most promising low-cost heuristics for solving the problem. The results obtained on a set of standard benchmark matrices show that the new hybrid heuristic method does not compare favorably with existing low-cost heuristics for profile reduction when applied to large-scale matrices.
The bandwidth minimization problem is a well-known NP-hard problem. This paper describes our experience in implementing a biased random-key genetic algorithm for the bandwidth reduction problem. Specifically, this pap...
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ISBN:
(纸本)9783030587994;9783030587987
The bandwidth minimization problem is a well-known NP-hard problem. This paper describes our experience in implementing a biased random-key genetic algorithm for the bandwidth reduction problem. Specifically, this paper compares the results of the new algorithm with the results yielded by four approaches. The results obtained on a set of standard benchmark matrices taken from the SuiteSparse sparse matrix collection indicated that the novel approach did not compare favorably with the state-of-the-art metaheuristic algorithm for bandwidth reduction. The former seems to be faster than the latter. On the other hand, the design of heuristics for bandwidth reduction is a very consolidated research area. Thus, a paradigm shift seems necessary to design a heuristic with better results than the state-of-the-art metaheuristic algorithm at shorter execution times.
Previous publications have reviewed the main algorithms for the identification of pseudoperipheral vertices in graphs. Based on this experience, this paper evaluates seven promising methods for solving the problem of ...
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ISBN:
(纸本)9781538692332
Previous publications have reviewed the main algorithms for the identification of pseudoperipheral vertices in graphs. Based on this experience, this paper evaluates seven promising methods for solving the problem of finding a proper pseudoperipheral vertex in a graph. This paper analyzes these seven pseudoperipheral vertex finders along with a new variant of Kaveh's B algorithm. This paper evaluates these algorithms with the purpose of identifying proper starting vertices for the Reverse Cuthill-McKee method. Extensive experiments among these pseudoperipheral vertex finders show that the George-Liu algorithm remains in the state of the practice to provide pseudoperipheral vertices to the Reverse Cuthill-McKee method when applied to matrices with symmetric sparsity patterns.
Computational and storage costs of resolution of large sparse linear systems Ax = b can be performed by reducing the bandwidth of A . Bandwidth reduction consists of carrying out permutations of lines an...
详细信息
Computational and storage costs of resolution of large sparse linear systems Ax = b can be performed by reducing the bandwidth of A . Bandwidth reduction consists of carrying out permutations of lines and columns so that they allow coefficients to remain near the main diagonal. When considering an adjacency matrix of a graph, bandwidth reduction can be considered in the sense of modifying the order in which the graph vertices are numbered. Heuristics for bandwidth reduction are revised in this study, aiming at determining which of them offers the higher bandwidth reduction with a reasonable computational cost. Specifically, metaheuristic-based heuristics are reviewed in this systematic review. Moreover, 29 metaheuristic-based heuristics tested for bandwidth reduction were found. Among them, 4 are recommended as possible state-of-the-art heuristics for addressing the problem.
In this work, a systematic review of heuristics for profile reduction of symmetric matrices is presented. 74 heuristics tested for reduction profile were found. Researchers compared results of their heuristics with re...
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In this work, a systematic review of heuristics for profile reduction of symmetric matrices is presented. 74 heuristics tested for reduction profile were found. Researchers compared results of their heuristics with results of other heuristics. In this review, these comparisons were analyzed and 8 heuristics were identified as the possible best for the problem. In addition, exchange methods, a form of local search, were identified that can benefit heuristics identified as the best ones for the task.
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