Finding Witnesses for Stability in the Hospitals/Residents Problem

• Item type: Journal(1)
• 公開日: 2015-02-15
• タイトル: Finding Witnesses for Stability in the Hospitals/Residents Problem
• タイトル / 言語: en
• タイトル: Finding Witnesses for Stability in the Hospitals/Residents Problem
• 言語: eng
• キーワード / 主題Scheme: Other
• キーワード / 主題: [一般論文（推薦論文）] the Hospitals/Residents problem, hospital's preference list, NP-complete, first-fit algorithm
• 資源タイプ / 資源タイプ識別子: http://purl.org/coar/resource_type/c_6501
• 資源タイプ: journal article
• 著者所属: Graduate School of Informatics, Kyoto University
• 著者所属: Academic Center for Computing and Media Studies, Kyoto University
• 著者所属: Graduate School of Informatics, Kyoto University
• 著者所属(英): en
• 著者所属(英): Graduate School of Informatics, Kyoto University
• 著者所属(英): en
• 著者所属(英): Academic Center for Computing and Media Studies, Kyoto University
• 著者所属(英): en
• 著者所属(英): Graduate School of Informatics, Kyoto University
• 著者名: Minseon, Lee; Shuichi, Miyazaki; Kazuo, Iwama
• 著者名(英): Minseon, Lee; Shuichi, Miyazaki; Kazuo, Iwama
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: The Hospitals/Residents problem is a many-to-one generalization of the well-known Stable Marriage problem. Its instance consists of a set of residents, a set of hospitals, each resident's preference list, each hospital's preference list, and each hospital's capacity (i.e., the number of available positions). It asks to find a stable matching between residents and hospitals. In this paper, we consider the problem of deciding, given residents' preference lists and a matching, whether there are hospitals' preference lists that make a given matching stable. We call this problem Stable Hospital's Preference List problem (SHPL). It is easy to see that there always exists a solution if we allow arbitrary preference lists of hospitals. Considering more suitable situations, we pose a restricted version, called k-SHPL, in which there are only k kinds of preference lists of hospitals. We show that 1-SHPL is solvable in polynomial time, while k-SHPL is NP-complete for any k such that 2 ≤ k ≤ n1-ε, where n is the number of residents and ε is any positive constant. We also present four heuristics algorithms (first-fit algorithms) for 2-SHPL. We implement these algorithms and present a computational study using random instances.; ------------------------------; This is a preprint of an article intended for publication Journal of; Information Processing(JIP). This preprint should not be cited. This; article should be cited as: Journal of Information Processing Vol.23(2015) No.2 (online); ------------------------------
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: The Hospitals/Residents problem is a many-to-one generalization of the well-known Stable Marriage problem. Its instance consists of a set of residents, a set of hospitals, each resident's preference list, each hospital's preference list, and each hospital's capacity (i.e., the number of available positions). It asks to find a stable matching between residents and hospitals. In this paper, we consider the problem of deciding, given residents' preference lists and a matching, whether there are hospitals' preference lists that make a given matching stable. We call this problem Stable Hospital's Preference List problem (SHPL). It is easy to see that there always exists a solution if we allow arbitrary preference lists of hospitals. Considering more suitable situations, we pose a restricted version, called k-SHPL, in which there are only k kinds of preference lists of hospitals. We show that 1-SHPL is solvable in polynomial time, while k-SHPL is NP-complete for any k such that 2 ≤ k ≤ n1-ε, where n is the number of residents and ε is any positive constant. We also present four heuristics algorithms (first-fit algorithms) for 2-SHPL. We implement these algorithms and present a computational study using random instances.; ------------------------------; This is a preprint of an article intended for publication Journal of; Information Processing(JIP). This preprint should not be cited. This; article should be cited as: Journal of Information Processing Vol.23(2015) No.2 (online); ------------------------------
• 書誌レコードID / 収録物識別子タイプ: NCID
• 書誌レコードID / 収録物識別子: AN00116647
• 書誌情報: 情報処理学会論文誌; 巻 56, 号 2, 発行日 2015-02-15
• ISSN / 収録物識別子タイプ: ISSN
• ISSN / 収録物識別子: 1882-7764