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整数解を導出するための単体法とゴモリーカットの合成について
http://hdl.handle.net/2237/23564
af839814-b124-4a7c-9822-f3245c584a16
名前 / ファイル | ライセンス | アクション | |
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Item type | 学術雑誌論文 / Journal Article(1) | |||||
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公開日 | 2016-02-23 | |||||
タイトル | ||||||
タイトル | 整数解を導出するための単体法とゴモリーカットの合成について | |||||
その他のタイトル | ||||||
その他のタイトル | On Composing the Simplex Method and Gomory Cut for Deriving Integer Assignments | |||||
著者 |
伏見, 政晃
× 伏見, 政晃× 西田, 直樹× 酒井, 正彦× 草刈, 圭一朗× 坂部, 俊樹× FUSHIMI, Masaaki× NISHIDA, Naoki× SAKAI, Masahiko× KUSAKARI, Keiichirou× SAKABE, Toshiki |
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権利 | ||||||
権利情報 | (c)一般社団法人電子情報通信学会 本文データは学協会の許諾に基づきCiNiiから複製したものである | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 単体法 | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | ゴモリーカット | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | SMTソルバ | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | simplex method | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Gomory cut | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | SMT solver | |||||
抄録 | ||||||
内容記述 | 与えられた有理数上の線形制約を充足する割り当てを求める手法として単体法がある.また,有理数解を求める手法と,ゴモリーカットをはじめとする切除平面法を組み合わせることで整数解を求められることが知られている.しかし,単体法を適用した後,必ずしもゴモリーカットが適用可能であるとは限らない.本稿では,ゴモリーカットの合成に必要な単体法における不変条件を示し,単体法とゴモリーカットを合成した手続きを示す.また,ゴモリーカットで追加する制約について,より単純な実装を行うための制約の形式を述べる.これらに基づいて,上記2つの手法を合成したソルバを実装し,評価する. The simplex method is one of the methods to derive rational assignments from linear constraints on ra- tiolals. It is known that we can derive integer assignments by composing the methods to derive rational assignments and cutting plane methods such as Gomory cut. However, Gomory cut is not applicable to all formulas resulted from the simplex method. In this paper, we first reveal an invariant property of the internal state of the simplex method in order to compose the simplex method and Gomory cut. Then we show a procedure of the composition of these methods, and we propose the form of constraints that are added into the initial constraint by applying Gomory cut so as to implement more simply. Finally, we compare our implemented solver with other solvers | |||||
内容記述タイプ | Abstract | |||||
出版者 | ||||||
出版者 | 一般社団法人電子情報通信学会 | |||||
言語 | ||||||
言語 | jpn | |||||
資源タイプ | ||||||
資源タイプresource | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | journal article | |||||
ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0913-5685 | |||||
書誌情報 |
電子情報通信学会技術研究報告. MSS, システム数理と応用 巻 112, 号 457, p. 109-114, 発行日 2013-02 |
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著者版フラグ | ||||||
値 | publisher | |||||
シリーズ | ||||||
関連名称 | ||||||
関連名称 | IEICE Technical Report;MSS2012-78 | |||||
シリーズ | ||||||
関連名称 | ||||||
関連名称 | IEICE Technical Report;SS2012-78 | |||||
URI | ||||||
識別子 | http://ci.nii.ac.jp/naid/110009712300/ | |||||
識別子タイプ | URI | |||||
URI | ||||||
識別子 | http://hdl.handle.net/2237/23564 | |||||
識別子タイプ | HDL |