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Title: An evaluation of low-cost heuristics for matrix bandwidth and profile reductions

Abstract

Hundreds of heuristics have been proposed to resolve the problems of bandwidth and profile reductions since the 1960s. We found 132 heuristics that have been applied to these problems in reviews of the literature. Among them, 14 were selected for which no other simulation or comparison revealed that the heuristic could be superseded by any other algorithm in the analyzed articles with respect to bandwidth or profile reduction. We also considered the computational costs of the heuristics during this process. Therefore, these 14 heuristics were selected as potentially being the best low-cost methods to solve the bandwidth and/or profile reduction problems. Results of the 14 selected heuristics are evaluated in this work. For evaluation on the set of test problems, a metric based on the relative percentage distance to the best possible bandwidth or profile is proposed. The most promising heuristics for several application areas are identified. Moreover, it was found that the FNCHC and GPS heuristics showed the best overall results in reducing the bandwidth of symmetric and asymmetric matrices among the evaluated heuristics, respectively. In addition, the NSloan and MPG heuristics showed the best overall results in reducing the profile of symmetric and asymmetric matrices among the heuristicsmore » among the evaluated heuristics, respectively.« less

Authors:
; ;  [1]
  1. Universidade Federal de Lavras (Brazil)
Publication Date:
OSTI Identifier:
22769352
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 2; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; ASYMMETRY; GLOBAL POSITIONING SYSTEM; MATRICES; METRICS; MINIMIZATION; SYMMETRY

Citation Formats

Gonzaga de Oliveira, Sanderson L., E-mail: sanderson@dcc.ufla.br, Bernardes, Júnior A. B.,, and Chagas, Guilherme O., E-mail: guilherme.chagas@computacao.ufla.br. An evaluation of low-cost heuristics for matrix bandwidth and profile reductions. United States: N. p., 2018. Web. doi:10.1007/S40314-016-0394-9.
Gonzaga de Oliveira, Sanderson L., E-mail: sanderson@dcc.ufla.br, Bernardes, Júnior A. B.,, & Chagas, Guilherme O., E-mail: guilherme.chagas@computacao.ufla.br. An evaluation of low-cost heuristics for matrix bandwidth and profile reductions. United States. doi:10.1007/S40314-016-0394-9.
Gonzaga de Oliveira, Sanderson L., E-mail: sanderson@dcc.ufla.br, Bernardes, Júnior A. B.,, and Chagas, Guilherme O., E-mail: guilherme.chagas@computacao.ufla.br. Tue . "An evaluation of low-cost heuristics for matrix bandwidth and profile reductions". United States. doi:10.1007/S40314-016-0394-9.
@article{osti_22769352,
title = {An evaluation of low-cost heuristics for matrix bandwidth and profile reductions},
author = {Gonzaga de Oliveira, Sanderson L., E-mail: sanderson@dcc.ufla.br and Bernardes, Júnior A. B., and Chagas, Guilherme O., E-mail: guilherme.chagas@computacao.ufla.br},
abstractNote = {Hundreds of heuristics have been proposed to resolve the problems of bandwidth and profile reductions since the 1960s. We found 132 heuristics that have been applied to these problems in reviews of the literature. Among them, 14 were selected for which no other simulation or comparison revealed that the heuristic could be superseded by any other algorithm in the analyzed articles with respect to bandwidth or profile reduction. We also considered the computational costs of the heuristics during this process. Therefore, these 14 heuristics were selected as potentially being the best low-cost methods to solve the bandwidth and/or profile reduction problems. Results of the 14 selected heuristics are evaluated in this work. For evaluation on the set of test problems, a metric based on the relative percentage distance to the best possible bandwidth or profile is proposed. The most promising heuristics for several application areas are identified. Moreover, it was found that the FNCHC and GPS heuristics showed the best overall results in reducing the bandwidth of symmetric and asymmetric matrices among the evaluated heuristics, respectively. In addition, the NSloan and MPG heuristics showed the best overall results in reducing the profile of symmetric and asymmetric matrices among the heuristics among the evaluated heuristics, respectively.},
doi = {10.1007/S40314-016-0394-9},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 2,
volume = 37,
place = {United States},
year = {2018},
month = {5}
}