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Experimental Evaluation of Approximation Algorithms for Maximum Distance-Bounded Subgraph Problems
http://hdl.handle.net/10228/0002000055
http://hdl.handle.net/10228/0002000055c74b0119-0414-4dd5-b86f-6f593f29061a
| 名前 / ファイル | ライセンス | アクション |
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10347454.pdf (640 KB)
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| アイテムタイプ | 学術雑誌論文 = Journal Article(1) | |||||||||||||||||
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| 公開日 | 2023-08-10 | |||||||||||||||||
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| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||||||||||
| 資源タイプ | journal article | |||||||||||||||||
| タイトル | ||||||||||||||||||
| タイトル | Experimental Evaluation of Approximation Algorithms for Maximum Distance-Bounded Subgraph Problems | |||||||||||||||||
| 言語 | en | |||||||||||||||||
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| 言語 | eng | |||||||||||||||||
| 著者 |
Asahiro, Yuichi
× Asahiro, Yuichi
× Kubo, Tomohiro
× 宮野, 英次
WEKO
6037
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| 内容記述タイプ | Other | |||||||||||||||||
| 内容記述 | In this paper we consider two distance-based relaxed variants of the maximum clique problem (MAX CLIQUE), named MAX d-CLIQUE and MAX d-CLUB: A d-clique in a graph G is a subset S ⊆ V(G) of vertices such that for pairs of vertices u, v ε S, the distance between u and v is at most d in G. A d-club in a graph G is a subset S' ⊆ V(G) of vertices that induces a subgraph of G of diameter at most d. MAX d-CLIQUE and MAX d-CLUB ask to find a maximum d-clique and a maximum d-club in a given unweighted graph, respectively. MAX 1-CLIQUE and MAX 1-CLUB cannot be efficiently approximated within a factor of n1-ε for any ε > 0 unless P = NP since they are identical to MAX CLIQUE [1], [2]. Also, it is known [3], [4] that it is NP-hard to approximate MAX d-CLIQUE and MAX d-CLUB to within a factor of n1/2-ε for any fixed d ≥ 2 and any ε > 0. As for approximability of MAX d-CLIQUE and MAX d-CLUB, [3] proposes a polynomial-time algorithm, called ByFindStard, and proves that its approximation ratio is O(n1/2) and O(n2/3) for any even d ≥ 2 and for any odd d ≥ 3, respectively. Very recently, a polynomial-time algorithm, called ByFindStar2d, achieving an optimal approximation ratio of O(n1/2) for MAX d-CLIQUE and MAX d-CLUB is designed for any odd d ≥ 3 in [4]. In this paper we implement those approximation algorithms and evaluate their quality empirically for random graphs Gn,p, which have n vertices and each edge appears with probability p. The experimental results show that (i) ByFindStar2d of approximation ratio O(n1/2) can find larger d-clubs (d-cliques) than ByFindStard of approximation ratio O(n2/3) for odd d, (ii) the size of d-clubs (d-cliques) output by ByFindStard is the same as ones by ByFindStar2d for even d, and (iii) ByFindStard can find the same size of d-clubs (d-cliques) much faster than ByFindStar2d. | |||||||||||||||||
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| 内容記述タイプ | Other | |||||||||||||||||
| 内容記述 | Joint 8th International Conference on Soft Computing and Intelligent Systems and 17th International Symposium on Advanced Intelligent Systems (SCIS&ISIS 2016), 25-28 August, 2016, Sapporo, Japan | |||||||||||||||||
| 書誌情報 |
2016 Joint 8th International Conference on Soft Computing and Intelligent Systems (SCIS) and 17th International Symposium on Advanced Intelligent Systems (ISIS) p. 892-897, 発行日 2016-12-26 |
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| 出版者 | IEEE | |||||||||||||||||
| DOI | ||||||||||||||||||
| 識別子タイプ | DOI | |||||||||||||||||
| 関連識別子 | https://doi.org/10.1109/SCIS-ISIS.2016.0193 | |||||||||||||||||
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| 識別子タイプ | ISBN | |||||||||||||||||
| 関連識別子 | 978-1-5090-2678-4 | |||||||||||||||||
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| 識別子タイプ | ISBN | |||||||||||||||||
| 関連識別子 | 978-1-5090-2679-1 | |||||||||||||||||
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| 権利情報 | Copyright (c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. | |||||||||||||||||
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| 出版タイプ | AM | |||||||||||||||||
| 出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||||||||||||||
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| 値 | yes | |||||||||||||||||
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| URL | https://hyokadb02.jimu.kyutech.ac.jp/html/233_ja.html | |||||||||||||||||
