1998 Fiscal Year Annual Research Report

グラフ・ネットワーク問題を解くアルゴリズムの開発

Research Project

Project/Area Number	10205213
Research Institution	Kyoto University
Principal Investigator	永持仁京都大学, 情報学研究科, 教授 (70202231)
Keywords	アルゴリズム / 連結度 / グラフ・ネットワーク / 最適化 / グラフ分割 / 最小カット / 劣モジュラ関数 / 近似アルゴリズム
Research Abstract	グラフの連結度問題はネットワークにおける信頼性問題や表データのセキュリティ問題に現れる.この問題に対し,いくつかの効率の良いアルゴリズムを得た.特に,提案するアルゴリズムによれば辺連結度と点連結度の増大を同時に考慮した新しいタイプの増大問題が多項式時間で解けるようになった.さらに,得られたアルゴリズムは,称劣モジュラ集合関数により一般化した問題に対しても作動するように拡張できることを示した.そのために、「正モジュラ性」という集合関数における新しい概念を導入し,その基本構造を明らかにした.さらに,連結度に関する問題として,グラフの最小3分割,4分割を行う高速アルゴリズムを設計した.特に,最小3分割アルゴリズムを拡張して対称劣モジュラ集合関数上での3分割問題が効率良く解けることも示した.

Research Products

(15 results)

All Other

All Publications (15 results)

[Publications] 永持,牧野,曽,村田,茨木: "初等的フローゲームの凸性について" 電子情報通信学会論文誌. J81-D-I. 666-676 (1998)
[Publications] A.Frank,T.Ibaraki,H.Nagamochi: "Two Arc-Disjoint Paths in Eularian Digraphs" SIAM J.Dicrete Mathematics. 11. 557-589 (1998)
[Publications] T.Ibaraki,A.Karzanov,H.Nagamochi: "A Fast Algorithm for Finding a Maximum Free Multiflow in an Inner Eulerian Network and Some Generalizations" Combinatorica. 18. 61-83 (1998)
[Publications] H.Nagamochi,T.Ibaraki: "A Note on Minimizing Submodular Functions" Information Processing Letters. 67. 239-244 (1998)
[Publications] T.Ishii,H.Nagamochi,T.Ibaraki: "Optimal Augmentation of a Biconnected Graph to nk-Edge-Connected an Tri-Conne grup〓" Proc.9th ACM-SIAM Symp.on Discrete Algorithms. 280-289 (1998)
[Publications] T.Hasunuma,H.Nagamochi: "Independent Spanning Trees with Small Depths in Iterated Line Digraphs" Australian Computer Science Communications,Computing Theory. 20. 21-35 (1998)
[Publications] H.Nagamochi,P.Eades: "Edge-Splitting and Edge-Connectivity Augmentation in Planar Graphs" Lecture Notes in Computer Science. 1412. 96-111 (1998)
[Publications] Y.Karuno,H.Nagamochi,T.Ibaraki: "A 1.5-Approxination for Single-Vehicle Scheduling Problem on a Line with Release and Handling Times" Proc.Japan-U.S.A.Symp.on Flexible Automation. 1363-1366 (1998)
[Publications] T.Ishii,H.Nagamochi,T.Ibaraki: "k-Edge and 3-Vertex Connectivity Augmentation in an Arbitrary Multigraph" Lecture Notes in Computer Science. 1533. 159-168 (1998)
[Publications] H.Nagamochi,T.Ibaraki: "Polyhedral Structure of Submodular and Posi-modular Systems" Lecture Notes in Computer Science. 1533. 169-178 (1998)
[Publications] H.Nagamochi,T.Hasunuma: "An Efficient NC Algorithm for a Sparse k-Edge-Connectivity Certificate" Lecture Notes in Computer Science. 1533. 447-456 (1998)
[Publications] H.Nagamochi,T.Ibaraki: "A Fast Algorithm for Computing Minimum 3-Way and 4-Way Cuts" Lecture Note in Computer Science,IPC099. (発表予定). (1999)
[Publications] H.Nagamochi,T.Ibaraki: "Augmenting Edge-Connectivity over the Entite Range in O(nm) Time" J.Algorithms. 30. 253-301 (1999)
[Publications] H.Nagamochi,T.Ibaraki: "An Approximation of the Minimum Vertex Cover in a Graph" J.Japan Society for Industrial and Applied Math.(掲載予定). (1999)
[Publications] 岩野和生,加藤直樹,永持仁: "アルゴリズム入門-設計と解析-(Computer Algorithms,sara Baaseの訳書)" アジソン・ウエスレイ社, 439 (1998)

1998 Fiscal Year Annual Research Report

グラフ・ネットワーク問題を解くアルゴリズムの開発

Principal Investigator

永持 仁 京都大学, 情報学研究科, 教授 (70202231)

Research Products

[Publications] 永持,牧野,曽,村田,茨木: "初等的フローゲームの凸性について" 電子情報通信学会論文誌. J81-D-I. 666-676 (1998)

[Publications] A.Frank,T.Ibaraki,H.Nagamochi: "Two Arc-Disjoint Paths in Eularian Digraphs" SIAM J.Dicrete Mathematics. 11. 557-589 (1998)

[Publications] T.Ibaraki,A.Karzanov,H.Nagamochi: "A Fast Algorithm for Finding a Maximum Free Multiflow in an Inner Eulerian Network and Some Generalizations" Combinatorica. 18. 61-83 (1998)

[Publications] H.Nagamochi,T.Ibaraki: "A Note on Minimizing Submodular Functions" Information Processing Letters. 67. 239-244 (1998)

[Publications] T.Ishii,H.Nagamochi,T.Ibaraki: "Optimal Augmentation of a Biconnected Graph to nk-Edge-Connected an Tri-Conne grup〓" Proc.9th ACM-SIAM Symp.on Discrete Algorithms. 280-289 (1998)

[Publications] T.Hasunuma,H.Nagamochi: "Independent Spanning Trees with Small Depths in Iterated Line Digraphs" Australian Computer Science Communications,Computing Theory. 20. 21-35 (1998)

[Publications] H.Nagamochi,P.Eades: "Edge-Splitting and Edge-Connectivity Augmentation in Planar Graphs" Lecture Notes in Computer Science. 1412. 96-111 (1998)

[Publications] Y.Karuno,H.Nagamochi,T.Ibaraki: "A 1.5-Approxination for Single-Vehicle Scheduling Problem on a Line with Release and Handling Times" Proc.Japan-U.S.A.Symp.on Flexible Automation. 1363-1366 (1998)

[Publications] T.Ishii,H.Nagamochi,T.Ibaraki: "k-Edge and 3-Vertex Connectivity Augmentation in an Arbitrary Multigraph" Lecture Notes in Computer Science. 1533. 159-168 (1998)

[Publications] H.Nagamochi,T.Ibaraki: "Polyhedral Structure of Submodular and Posi-modular Systems" Lecture Notes in Computer Science. 1533. 169-178 (1998)

[Publications] H.Nagamochi,T.Hasunuma: "An Efficient NC Algorithm for a Sparse k-Edge-Connectivity Certificate" Lecture Notes in Computer Science. 1533. 447-456 (1998)

[Publications] H.Nagamochi,T.Ibaraki: "A Fast Algorithm for Computing Minimum 3-Way and 4-Way Cuts" Lecture Note in Computer Science,IPC099. (発表予定). (1999)

[Publications] H.Nagamochi,T.Ibaraki: "Augmenting Edge-Connectivity over the Entite Range in O(nm) Time" J.Algorithms. 30. 253-301 (1999)

[Publications] H.Nagamochi,T.Ibaraki: "An Approximation of the Minimum Vertex Cover in a Graph" J.Japan Society for Industrial and Applied Math.(掲載予定). (1999)

[Publications] 岩野和生,加藤直樹,永持 仁: "アルゴリズム入門-設計と解析-(Computer Algorithms,sara Baaseの訳書)" アジソン・ウエスレイ社, 439 (1998)

永持仁京都大学, 情報学研究科, 教授 (70202231)

[Publications] 岩野和生,加藤直樹,永持仁: "アルゴリズム入門-設計と解析-(Computer Algorithms,sara Baaseの訳書)" アジソン・ウエスレイ社, 439 (1998)