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このアイテムのファイル:
ファイル | 記述 | サイズ | フォーマット | |
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LIPIcs.APPROX-RANDOM.2015.361.pdf | 545 kB | Adobe PDF | 見る/開く |
タイトル: | A Tight Approximation Bound for the Stable Marriage Problem with Restricted Ties |
著者: | Huang, Chien-Chung Iwama, Kazuo Miyazaki, Shuichi https://orcid.org/0000-0003-0369-1970 (unconfirmed) Yanagisawa, Hiroki |
著者名の別形: | 岩間, 一雄 宮崎, 修一 柳澤, 弘揮 |
キーワード: | stable marriage with ties and incomplete lists approximation algorithm integer program linear program relaxation integrality gap |
発行日: | 2015 |
出版者: | Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik |
誌名: | Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015) |
巻: | 40 |
開始ページ: | 361 |
終了ページ: | 380 |
抄録: | The problem of finding a maximum cardinality stable matching in the presence of ties and unacceptable partners, called MAX SMTI, is a well-studied NP-hard problem. The MAX SMTI is NP-hard even for highly restricted instances where (i) ties appear only in women's preference lists and (ii) each tie appears at the end of each woman's preference list. The current best lower bounds on the approximation ratio for this variant are 1.1052 unless P=NP and 1.25 under the unique games conjecture, while the current best upper bound is 1.4616. In this paper, we improve the upper bound to 1.25, which matches the lower bound under the unique games conjecture. Note that this is the first special case of the MAX SMTI where the tight approximation bound is obtained. The improved ratio is achieved via a new analysis technique, which avoids the complicated case-by-case analysis used in earlier studies. As a by-product of our analysis, we show that the integrality gap of natural IP and LP formulations for this variant is 1.25. We also show that the unrestricted MAX SMTI cannot be approximated with less than 1.5 unless the approximation ratio of a certain special case of the minimum maximal matching problem can be improved. |
著作権等: | Since 2013, documents stored on DROPS are typically published under a CC-BY Creative Commons Attribution 3.0 Unported license. The authoritative license is always the one given in the PDF. |
URI: | http://hdl.handle.net/2433/200620 |
出現コレクション: | 学術雑誌掲載論文等 |
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