2003 年度実績報告書

グラフ理論に基づく近似アルゴリズムの構築とネットワーク問題への応用

研究課題

研究課題/領域番号	14580372
研究機関	豊橋技術科学大学
研究代表者	永持仁豊橋技術科学大学, 工学部, 教授 (70202231)
研究分担者	軽野義行京都工芸繊維大学, 工芸学部, 助手 (80252542) 石井利昌豊橋技術科学大学, 工学部, 助手 (30324487)
キーワード	近似アルゴリズム / グラフ連結度 / スケジューリング問題 / 矩形分割問題 / 供給点配置問題 / 連結度増大問題 / 耐故障性 / ネットワークトポロジー
研究概要	与えられたグラフに最小本数の枝を付加して,点/枝連結度を指定された値にまで増大させる問題は,連結度増大問題と呼ばれている.連結なグラフにおいて2節点間ごとに局所点連結度を2に増大させるか否かの要求の指定がある場合,この問題がNP-困難であることを示し,最適解の大きさの1.5倍以内の解を求める近似アルゴリズムを設計した.グラフモデルにおいて連結度,すなわちつながりの強さは,ネットワークの耐故障性に対応する.グラフの枝付加問題において,距離を指定した値以下に抑えることを目的とした問題は,がNP-困難になるだけでなく,定数倍近似のアルゴリズムを設計することも難しくなることが知られている.与えられたグラフが木である場合,木の直径を目標値以下にするような最小の付加枝集合を求める問題に対し,目標値が奇数の場合に,8倍近似アルゴリズムが設計できることを示し,さらに,距離の制約に加え,2点連結化の要求も与えられた場合には,4倍近似のアルゴリズムが得られることを示した.供給点配置問題とは,各節点には非負の重みがあり,要求を満たす供給点集合のうちで重み和を最小するものを求める問題であり,これまで,各節点ごとに,供給点集合との問の節点領域点連結度の要求値が異なっている問題は未解決であったが,個数最小化問題は,要求値として3,4の値を許した場合にNP-困難になり,要求値が0,1,2,3のいずれかである場合には多項式時間で解けることを示した. この他,機械スケジューリング問題,矩形分割問題,部分木被服問題,2階層描画における交差点数最小化問題に対して,従来よりも高い近似性能を保証する近似アルゴリズムを設計した.

研究成果
(24件)

すべてその他

すべて文献書誌 (24件)

[文献書誌] H.Nagamochi, K.Suzuki, T.Ishii: "A simple recognition of maximal planar graphs"Information Processing Letters. vol.89, no.5. 223-226 (2004)
[文献書誌] Y.Karuno, H.Nagamochi: "An approximability result of the multi-vehicle scheduling problem on a path with release and handling times"Theoretical Computer Science A. vol.312, issues 2-3. 267-280 (2004)
[文献書誌] H.Nagamochi, Y.Nishida, T.Ibaraki: "Approximability of the minimum maximal in matching problem in planar graphs"Inst.Electron.Inform.Comm.Eng.Trans.Fundamentals. Vol.E86-A, No.12. 3251-3258 (2003)
[文献書誌] H.Nagamochi, P.Eades: "An edge-splitting algorithm in planar graphs"J.Combinatorial Optimization. vol.7. 137-159 (2003)
[文献書誌] H.Nagamochi, T.Ishii: "On the minimum local-vertex-connectivity augmentation in graphs"Discrete Applied Mathematics. vol.129/2. 475-486 (2003)
[文献書誌] Y.Karuno, H.Nagamochi: "2-approximation algorithms for the multi-vehicle scheduling on a path with release and handling times"Discrete Applied Mathematics. vol.129/2. 433-447 (2003)
[文献書誌] L.Zhao, H.Nagamochi, T.Ibaraki: "A linear time 5/3-approximation for the minimum strongly-connected spanning subgraph problem"Information Processing Letters. vol.86/2. 63-70 (2003)
[文献書誌] H.Nagamochi, S.Nakamura, T.Ishii: "Constructing a cactus for minimum cuts of a graph in O(mn+n^2log n) time and O(m) space"Inst.Electron.Inform.Comm.Eng.Trans.Fundamentals. vol.E86-D, no.2. 179-185 (2003)
[文献書誌] H.Nagamochi: "Algorithms for the minimum partitioning problems in graphs"Inst.Electron.Inform.Comm.Eng.Trans.Fundamentals. Vol.J86-D-1. 53-68 (2003)
[文献書誌] L.Zhao, H.Nagamochi, T.Ibaraki: "A primal-dual approximation algorithm for the survivable network design problem in hypergraphs"Discrete Applied Mathematics. vol.126/2-3. 275-289 (2003)
[文献書誌] H.Ito, H.Nagamochi: "Comparing hypergraphs by areas of hyperedges drawn on a convex polygon"Lecture Notes in Computer Science. Vol.2866. 176-181 (2003)
[文献書誌] H.Ito, H.Nagamochi: "Can a hypergraph cover every convex polygon?"The 3rd Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications. 293-302 (2003)
[文献書誌] T.Ishii, H.Fujita, H.Nagamochi: "Source location problem with local 3-vertex-connectivity requirements"The 3rd Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications. 368-377 (2003)
[文献書誌] H.Nagamochi: "Computing extreme sets in graphs and its applications"The 3rd Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications. 349-357 (2003)
[文献書誌] T.Ishii, Y.Akiyama, H.Nagamochi: "Minimum augmentation of edge-connectivity between vertices and sets of vertices in undirected graphs"ENTCS (Elsevier Science in the series Electronic Notes in Theoretical Computer Science) Computing : The Australasian Theory Symposium, CATS 2003. (掲載決定). (2003)
[文献書誌] H.Nagamochi, K.Suzuki, T.Ishii: "A simple recognition of maximal planar graphs"Proceedings of the 7^<th> Japan-Korea Joint Workshop on Algorithms and Computation. 182-188 (2003)
[文献書誌] H.Nagamochi, N.Yamada: "Fast algorithms for counting bilayer crossings"Proceedings of the 7^<th> Japan-Korea Joint Workshop on Algorithms and Computation. 203-209 (2003)
[文献書誌] H.Nagamochi, K.Iwata, T.Ishii: "A simple and robust algorithm for bisecting a triconnected graph with two resource sets"Proceedings of the 7^<th> Japan-Korea Joint Workshop on Algorithms and Computation. 210-222 (2003)
[文献書誌] H.Nagamochi: "An improved approximation to the one-sided bilayer drawing"Lecture Notes in Computer Science. vol.2912. 406-418 (2004)
[文献書誌] H.Nagamochi, K.Kuroya: "Convex drawing for c-planar biconnected clustered graphs"Lecture Notes in Computer Science. vol.2912. 369-380 (2004)
[文献書誌] H.Nagamochi, K.Okada: "Polynomial time 2-approximation algorithms for the minmax subtree cover problem"Lecture Notes in Computer Science. vol.2906. 138-147 (2003)
[文献書誌] H.Nagamochi, Y.Abe: "An approximation algorithm for dissecting a rectangle into rectangles with specified areas"Lecture Notes in Computer Science. vol.2906. 280-289 (2003)
[文献書誌] Y.Karuno, H.Nagamochi: "A better approximation for the two-machine flowshop scheduling problem with time lags"Lecture Notes in Computer Science. vol.2906. 309-318 (2003)
[文献書誌] T.Ishii, S.Yamamoto, H.Nagamochi: "Augmenting forests to meet odd diameter requirements"Lecture Notes in Computer Science. vol.2906. 434-443 (2003)

2003 年度 実績報告書

グラフ理論に基づく近似アルゴリズムの構築とネットワーク問題への応用

研究代表者

永持 仁 豊橋技術科学大学, 工学部, 教授 (70202231)

研究成果

[文献書誌] H.Nagamochi, K.Suzuki, T.Ishii: "A simple recognition of maximal planar graphs"Information Processing Letters. vol.89, no.5. 223-226 (2004)

[文献書誌] Y.Karuno, H.Nagamochi: "An approximability result of the multi-vehicle scheduling problem on a path with release and handling times"Theoretical Computer Science A. vol.312, issues 2-3. 267-280 (2004)

[文献書誌] H.Nagamochi, Y.Nishida, T.Ibaraki: "Approximability of the minimum maximal in matching problem in planar graphs"Inst.Electron.Inform.Comm.Eng.Trans.Fundamentals. Vol.E86-A, No.12. 3251-3258 (2003)

[文献書誌] H.Nagamochi, P.Eades: "An edge-splitting algorithm in planar graphs"J.Combinatorial Optimization. vol.7. 137-159 (2003)

[文献書誌] H.Nagamochi, T.Ishii: "On the minimum local-vertex-connectivity augmentation in graphs"Discrete Applied Mathematics. vol.129/2. 475-486 (2003)

[文献書誌] Y.Karuno, H.Nagamochi: "2-approximation algorithms for the multi-vehicle scheduling on a path with release and handling times"Discrete Applied Mathematics. vol.129/2. 433-447 (2003)

[文献書誌] L.Zhao, H.Nagamochi, T.Ibaraki: "A linear time 5/3-approximation for the minimum strongly-connected spanning subgraph problem"Information Processing Letters. vol.86/2. 63-70 (2003)

[文献書誌] H.Nagamochi, S.Nakamura, T.Ishii: "Constructing a cactus for minimum cuts of a graph in O(mn+n^2log n) time and O(m) space"Inst.Electron.Inform.Comm.Eng.Trans.Fundamentals. vol.E86-D, no.2. 179-185 (2003)

[文献書誌] H.Nagamochi: "Algorithms for the minimum partitioning problems in graphs"Inst.Electron.Inform.Comm.Eng.Trans.Fundamentals. Vol.J86-D-1. 53-68 (2003)

[文献書誌] L.Zhao, H.Nagamochi, T.Ibaraki: "A primal-dual approximation algorithm for the survivable network design problem in hypergraphs"Discrete Applied Mathematics. vol.126/2-3. 275-289 (2003)

[文献書誌] H.Ito, H.Nagamochi: "Comparing hypergraphs by areas of hyperedges drawn on a convex polygon"Lecture Notes in Computer Science. Vol.2866. 176-181 (2003)

[文献書誌] H.Ito, H.Nagamochi: "Can a hypergraph cover every convex polygon?"The 3rd Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications. 293-302 (2003)

[文献書誌] T.Ishii, H.Fujita, H.Nagamochi: "Source location problem with local 3-vertex-connectivity requirements"The 3rd Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications. 368-377 (2003)

[文献書誌] H.Nagamochi: "Computing extreme sets in graphs and its applications"The 3rd Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications. 349-357 (2003)

[文献書誌] H.Nagamochi, K.Suzuki, T.Ishii: "A simple recognition of maximal planar graphs"Proceedings of the 7^<th> Japan-Korea Joint Workshop on Algorithms and Computation. 182-188 (2003)

[文献書誌] H.Nagamochi, N.Yamada: "Fast algorithms for counting bilayer crossings"Proceedings of the 7^<th> Japan-Korea Joint Workshop on Algorithms and Computation. 203-209 (2003)

[文献書誌] H.Nagamochi, K.Iwata, T.Ishii: "A simple and robust algorithm for bisecting a triconnected graph with two resource sets"Proceedings of the 7^<th> Japan-Korea Joint Workshop on Algorithms and Computation. 210-222 (2003)

[文献書誌] H.Nagamochi: "An improved approximation to the one-sided bilayer drawing"Lecture Notes in Computer Science. vol.2912. 406-418 (2004)

[文献書誌] H.Nagamochi, K.Kuroya: "Convex drawing for c-planar biconnected clustered graphs"Lecture Notes in Computer Science. vol.2912. 369-380 (2004)

[文献書誌] H.Nagamochi, K.Okada: "Polynomial time 2-approximation algorithms for the minmax subtree cover problem"Lecture Notes in Computer Science. vol.2906. 138-147 (2003)

[文献書誌] H.Nagamochi, Y.Abe: "An approximation algorithm for dissecting a rectangle into rectangles with specified areas"Lecture Notes in Computer Science. vol.2906. 280-289 (2003)

[文献書誌] Y.Karuno, H.Nagamochi: "A better approximation for the two-machine flowshop scheduling problem with time lags"Lecture Notes in Computer Science. vol.2906. 309-318 (2003)

[文献書誌] T.Ishii, S.Yamamoto, H.Nagamochi: "Augmenting forests to meet odd diameter requirements"Lecture Notes in Computer Science. vol.2906. 434-443 (2003)

2003 年度実績報告書

永持仁豊橋技術科学大学, 工学部, 教授 (70202231)