| アイテムタイプ |
学術雑誌論文 = Journal Article(1) |
| 公開日 |
2023-08-10 |
| 資源タイプ |
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資源タイプ識別子 |
http://purl.org/coar/resource_type/c_6501 |
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資源タイプ |
journal article |
| タイトル |
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タイトル |
Optimal Approximation Algorithms for Maximum Distance-Bounded Subgraph Problems |
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言語 |
en |
| 言語 |
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|
言語 |
eng |
| 著者 |
Asahiro, Yuichi
Doi, Yuya
宮野, 英次
Samizo, Kazuaki
Shimizu, Hirotaka
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| 抄録 |
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内容記述タイプ |
Abstract |
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内容記述 |
In this paper we study the (in)approximability of 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 = (V,E) is a subset S ⊆ V of vertices such that for every pair of vertices u, v ∈ S, the distance between u and v is at most d in G. A d-club in a graph G = (V,E) is a subset S_ ⊆ V of vertices that induces a subgraph of G of diameter at most d. Given a graph G with n vertices, the goal of Max d-Clique (Max d-Club, resp.) is to find a d-clique (d-club, resp.) of maximum cardinality in G. Since Max 1- Clique and Max 1-Club are identical to Max Clique, the inapproximabilty for Max Clique shown by Zuckerman in 2007 is transferred to them. Namely, Max 1-Clique and Max 1-Club cannot be efficiently approximated within a factor of n1−ε for any ε > 0 unless P = NP. Also, in 2002, Marincek and Mohar showed that it is NP-hard to approximate Max d-Club to within a factor of n1/3−ε for any ε > 0 and any fixed d ≥ 2. In this paper, we strengthen the hardness result; we prove that, for any ε > 0 and any fixed d ≥ 2, it is NP-hard to approximate Max d-Club to within a factor of n1/2−ε. Then, we design a polynomial-time algorithm which achieves an optimal approximation ratio of O(n1/2) for any integer d ≥ 2. By using the similar ideas, we show the O(n1/2)-approximation algorithm for Max d-Clique for any d ≥ 2. This is the best possible in polynomial time unless P = NP, as we can prove the Ω(n1/2−ε)-inapproximability. |
| 書誌情報 |
en : Algorithmica
巻 80,
号 6,
p. 1834-1856,
発行日 2017-07-21
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| 出版社 |
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出版者 |
Springer |
| DOI |
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識別子タイプ |
DOI |
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関連識別子 |
https://doi.org/10.1007/s00453-017-0344-y |
| NCID |
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収録物識別子タイプ |
NCID |
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収録物識別子 |
AA10679010 |
| ISSN |
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収録物識別子タイプ |
PISSN |
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収録物識別子 |
0178-4617 |
| ISSN |
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収録物識別子タイプ |
EISSN |
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収録物識別子 |
1432-0541 |
| 著作権関連情報 |
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権利情報 |
Copyright (c) Springer Science+Business Media, LLC 2017 |
| キーワード |
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主題Scheme |
Other |
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主題 |
d-clique |
| キーワード |
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|
主題Scheme |
Other |
|
主題 |
d-club |
| キーワード |
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|
主題Scheme |
Other |
|
主題 |
Maximum distance-bounded subgraph problems |
| キーワード |
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主題Scheme |
Other |
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主題 |
(In)approximability |
| 出版タイプ |
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出版タイプ |
AM |
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出版タイプResource |
http://purl.org/coar/version/c_ab4af688f83e57aa |
| 査読の有無 |
|
|
値 |
yes |
| 研究者情報 |
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|
URL |
https://hyokadb02.jimu.kyutech.ac.jp/html/233_ja.html |
10315887.pdf (241 KB)
