離散最適化アルゴリズムの計算効率と離散構造

2000 Fiscal Year Annual Research Report

• Project/Area Number: 10205217
• Research Institution: Osaka University
• Principal Investigator: 藤重 悟 大阪大学, 基礎工学研究科, 教授 (10092321)
• Co-Investigator(Kenkyū-buntansha): 繁野 麻衣子 筑波学大学, 社会工学系, 講師 (40272687) ; 牧野 和久 大阪大学, 基礎工学研究科, 講師 (60294162) ; 岩田 覚 東京大学, 大学院・工学系研究科, 助教授 (00263161) ; 高畑 貴志 大阪大学, 基礎工学研究科, 助手 (50324827)
• Keywords: 計算効率 / アルゴリズム / 劣モジュラ関数 / ネットワーク最適化 / コテリ理論

Research Abstract

本研究班では,比較的容易に解くことのできる離散最適化問題の離散構造を詳細に調べ,効率的なアルゴリズムを設計するための統一的な指針を与えることを目的として,ネットワーク,マトロイド,論理関数に関する理論的な研究を続けてきた.本年度に得られた主要な成果としては,劣モジュラ関数最小化に対する加減算と比較のみを用いた完全に組合せ的なアルゴリズムの開発,
Iwata,S.: A fully combinatorial algorithm for submodular function Minimization.Journal of Combi-natorial Theory,submitted.
および,劣モジュラ関数の一般化である双劣モジュラ関数最小化に関する組合せ的多項式時間アルゴリズムの開発
Fujishige,S.and Iwata,S.: Bisubmodular function minimization.情報処理学会研究報告2000-AL-75(2000),53-60.
が挙げられる.さらに,ネットワーク上の最適化問題としては,
Arata,K.,Iwata,S.,Makino,K.,and Fiujishige,S.: Locating sources to meet flow demands in undirected networks.SWAT2000,LNCS1851(2000),300-313.
においてフロー要求を実現するような最適施設配置問題に対するアルゴリズムを提案し,その計算量を明らかにした.また,最小カットに対する逆最適化問題に対して,パラメトリック手法を用いた高速なアルゴリズムを開発した.その他にも複基多面体の特徴付け,劣モジュラ構造に注目した経済均衡解析,論理関数を用いた分散システムにおける最適コテリの構築等を行った.

Research Products

• [Publications] Fujishige,S.: "Realization of set functions as cut functions of graphs and hypergraphs"Discrete Mathematics. 226. 199-210 (2001)
• [Publications] Fujishige,S.: "Notes on L-/M-convex functions and the separation theorems"Mathematical Programming. 88. 129-146 (2000)
• [Publications] Fujishige,S.: "A note on Faigle and Kern's dual greedy polyhedra"Mathematical Programming. 88. 217-220 (2000)
• [Publications] Fujishige,S.: "An algorithm for solving the minimum norm point over the intersection of a polytope and an affine set"Journal of Optimization Theory and Applications. 105. 113-141 (2000)
• [Publications] Fujishige,S.: "Algorithms for submodular flows"IEICE Transactions on Information and Systems. E83-D. 322-329 (2000)
• [Publications] Fujishige,S.: "A laminarity property of the polyhedron described by a weakly posi-modular set function"Discrete Applied Mathematics. 100. 123-126 (2000)
• [Publications] Iwata,S.: "A combinatorial strongly polynomial algorithm for minimizing submodular functions"Journal of the ACM. (採録決定済).
• [Publications] Eiter,T.: "On the difference of Horn theories"Journal of Computer and System Sciences. 61. 478-507 (2000)
• [Publications] Makino,K.: "Efficient generation of all regular non-dominated coteries"Proceedings of PODC2000. 19. 279-288 (2000)
• [Publications] Boros,E.: "Generating partial and multiple transversals of a hypergraph"ICALP2000,LNCS. 1853. 588-599 (2000)
• [Publications] Makino,K.: "Max- and min-neighborhood monopolies"SWAT2000,LNCS. 1851. 513-526 (2000)
• [Publications] Arata,K.: "Locating sources to meet flow demands in undirected networks"SWAT2000,LNCS. 1851. 300-313 (2000)
• [Publications] Shigeno,M.: "Relaxed most negative cycle and most positive cut canceling algorithms for minimum cost flow"Mathematics of Operations Research. 25. 76-104 (2000)
• [Publications] Iwata,S.: "A fast cost scaling algorithm for submodular flow"Information Proceeding Letters. 74. 123-128 (2000)
• [Publications] Iwata,S.: "Fast cycle canceling algorithms for minimum cost submodular flow"Combinatorica. (採録決定済).
• [Publications] Iwata,S.: "Conjugate scaling technique for Fenchel-type duality in discrete convex optimization"SIAM Journal on Optimization. (採録決定済).
• [Publications] Iwata,S.: "Combinatorial relaxation algorithm for mixed polynomial matrices"Mathematical Programming. (採録決定済).
• [Publications] Iwata,S.: "On matroid intersection adjacency"Discrete Mathematics. (採録決定済).
• [Publications] Ono,H.: "Logical analysis of data with decomposable structures"COCOON2000,LNCS. 1858. 396-406 (2000)
• [Publications] Boros,E.: "Fully consistent extensions of partially defined Boolean functions with missing bits"IFIP TCS2000,LNCS. 1872. 257-272 (2000)
• [Publications] Boros,E.: "Finding essential attributes in binary data"IDEAL2000,LNCS. 1983. 133-138 (2000)
• [Publications] Makino,K.: "On minimum edge ranking spanning trees"Journal of Algorithms. (採録決定済).
• [Publications] Boros,E.: "Dual-bounded generating problems : partial and multiple transversals of a hypergraph"SIAM Journal on Computing. (採録決定済).
• [Publications] Eiter,T.: "Decision lists and related Boolean functions"Theoretical Computer Science. (採録決定済).
• [Publications] Ibaraki,T.: "On functional dependencies in q-Horn theories"Artificial Intelligence. (採録決定済).
• [Publications] Makino,K.: "A linear time algorithm for recognizing regular Boolean functions"Journal of Algorithms. (採録決定済).
• [Publications] Eiter,T.: "Disjunctions of Horn theories and their cores"SIAM Journal on Computing. (採録決定済).