Development of Efficient and Accurate Approximation Algorithms for Constrained Optimization of Discrete Convex Functions

• Project/Area Number: 21740060
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Tohoku University
• Principal Investigator: SHIOURA Akiyoshi 東北大学, 大学院・情報科学研究科, 准教授 (10296882)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 離散最適化 / 組合せ最適化 / 数理計画 / 離散凸関数 / 近似アルゴリズム / アルゴリズム / マトロイド / 劣モジュラ関数 / マトロスド

Research Abstract

The aim of this research is to develop algorithms with theoretical guarantee for both of computational time and quality of solutions by using the theory of discrete convex analysis. During the three years of the research period, I have obtained various new results. In particular, I developed a polynomial-time approximation scheme for the maximization of an M-concave function under multiple knapsack constraints. In addition, I revealed the structure of a general solution set called a neighbor system, and showed that the minimization of a separable-convex function over a neighbor system can be solved in polynomial time.

Research Products

• [Journal Article] Neighbor Systems, Jump Systems, and Bisubmodular Polyhedra (2012)
  • Author(s): A. Shioura
  • Journal Title: SIAM Journal on Discrete Mathematics Volume: 26 Pages: 114-144
  • Peer Reviewed
• [Journal Article] Optimal Allocation Problem with Quadratic Utility Functions and Its Relationship with Graph Cut Problem (2012)
  • Author(s): A. Shioura, S. Suzuki
  • Journal Title: Journal of Operations Research Society of Japan Volume: 55 Pages: 92-105
  • NAID: 110009436529
  • Peer Reviewed
• [Journal Article] M-convex Function Minimization by Continuous Relaxation Approach : Proximity Theorem and Algorithm (2011)
  • Author(s): S. Moriguchi, A. Shioura, N. Tsuchimura
  • Journal Title: SIAM Journal on Optimization Volume: 21 Pages: 633-668
  • Peer Reviewed
• [Journal Article] M-convex Function Minimization by Continuous Relaxation Approach…Proximity Theorem and Algorithm… (2011)
  • Author(s): Satoko Moriguchi, Akiyoshi Shioura, Nobuyuki Tsuchimura
  • Journal Title: SIAM Journal on Optimization Volume: 21 Pages: 633-668
  • Peer Reviewed
• [Journal Article] A Fast Algorithm for Computing a Nearly Equitable Edge Coloring with Balanced Conditions (2010)
  • Author(s): A. Shioura, M. Yagiura
  • Journal Title: Journal of Graph Algorithms and Applications Volume: 13 Pages: 391-407
  • Peer Reviewed
• [Journal Article] A Fast Algorithm for Computing a Nearly Equitable Edge Coloring with Balanced Conditions (2010)
  • Author(s): Akiyoshi Shioura, Mutsunori Yagiura
  • Journal Title: Journal of Graph Algorithms and Applications Volume: 14 Pages: 391-407
  • Peer Reviewed
• [Journal Article] Single Machine Scheduling with Controllable Processing Times by Submodular Optimization (2009)
  • Author(s): N. Shakhlevich, A. Shioura, V. Strusevich
  • Journal Title: International Journal of Foundations of Computer Science Volume: 20 Pages: 247-269
  • Peer Reviewed
• [Journal Article] New Algorithms for Convex Cost Tension Problem with Application to Computer Vision (2009)
  • Author(s): V. Kolmogorov, A. Shioura
  • Journal Title: Discrete Optimization Volume: 6 Pages: 378-393
  • Peer Reviewed
• [Journal Article] Single Machine Scheduling with Controllable Processing Times by Submodular Optimization (2009)
  • Author(s): Natalia Shakhlevich, Akiyoshi Shioura, Vitaly Strusevich
  • Journal Title: International Journal of Foundations of Computer Science 20 Pages: 247-269
  • Peer Reviewed
• [Journal Article] New Algorithms for Convex Cost Tension Problem with Application to Computer Vision (2009)
  • Author(s): Vladimir Kolmogorov, Akiyoshi Shioura
  • Journal Title: Discrete Optimization 6 Pages: 378-393
  • Peer Reviewed
• [Presentation] Computing the Convex Closure of Discrete Convex Functions (2012)
  • Author(s): A. Shioura
  • Organizer: Workshop on Modern Aspects of Submodularity
  • Place of Presentation: アトランタ, アメリカ
  • Year and Date: 2012-03-20
• [Presentation] Computing the Convex Closure of Discrete Convex Functions (2012)
  • Author(s): Akiyoshi Shioura
  • Organizer: Workshop on Modern Aspects of Submodularity
  • Place of Presentation: アトランタ,アメリカ(招待講演)
  • Year and Date: 2012-03-20
• [Presentation] Polynomial-Time Approximation Scheme for Maximizing Gross Substitutes Utility under Budget Constraints (2011)
  • Author(s): A. Shioura
  • Organizer: 19th Annual European Symposium on Algorithms(ESA 2011)
  • Place of Presentation: ザールブリュッケン, ドイツ
  • Year and Date: 2011-09-05
• [Presentation] Polynomial-Time Approximation Scheme for Maximizing Gross Substitutes Utility under Budget Constraints (2011)
  • Author(s): Akiyoshi Shioura
  • Organizer: 19th Annual European Symposium on Algorithms (ESA 2011)
  • Place of Presentation: ザールブリュッケン,ドイツ
  • Year and Date: 2011-09-05
• [Presentation] Polynomial-Time Approximation Scheme for Maximizing M.-concave Functions under Budget Constraints (2011)
  • Author(s): A. Shioura
  • Organizer: 7th Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications
  • Place of Presentation: 京都大学
  • Year and Date: 2011-06-01
• [Presentation] Polynomial-Time Approximation Scheme for Maximizing M〓-concave Functions under Budget Constraints (2011)
  • Author(s): Akiyoshi Shioura
  • Organizer: 7th Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications
  • Place of Presentation: 京都大学
  • Year and Date: 2011-06-01
• [Presentation] Polynomial-Time Approximation Scheme for Maximizing Gross Substitutes Utility under Budget Constraints (2011)
  • Author(s): A. Shioura
  • Organizer: NII Shonan Meeting on Graph Algorithms and Combinatorial Optimization
  • Place of Presentation: 湘南国際村センター(神奈川県葉山町)
  • Year and Date: 2011-02-15
• [Presentation] Neighbor Systems, Jump Systems, and Bisubmodular Polyhedra (2010)
  • Author(s): A. Shioura
  • Organizer: International Symposium on Algorithms and Computation (ISAAC)2010
  • Place of Presentation: ラマダプラザ済州ホテル(大韓民国済州島)
  • Year and Date: 2010-12-15
• [Presentation] Neighbor Systems, Jump Systems, and Bisubmodular Polyhedra (2010)
  • Author(s): Akiyoshi Shioura
  • Organizer: International Symposium on Algorithms and Computation (ISAAC) 2010
  • Place of Presentation: ラマダプラザ済州ホテル(大韓民国済州島)
  • Year and Date: 2010-12-15
• [Presentation] A Decomposition Algorithm for Linear Optimization Over Polymatroids with Applications (2009)
  • Author(s): N. Shakhlevich, A. Shioura, V. Strusevich
  • Organizer: 20th International Symposium on Mathematical Programming
  • Place of Presentation: シカゴ, アメリカ
  • Year and Date: 2009-08-25
• [Presentation] A Divide-and-Conquer Approach for Polymatroid Optimization with Application to Preemptive Scheduling Problems (2009)
  • Author(s): N. Shakhlevich, A. Shioura, V. Strusevich
  • Organizer: 6th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications
  • Place of Presentation: ブダペスト, ハンガリー
  • Year and Date: 2009-05-09
• [Presentation] A divide-and-conquer approach for polymatroid optimization with application to preemptive scheduling problems (2009)
  • Author(s): Natalia Shakhlevich, Akiyoshi Shioura, Vitaly Strusevich
  • Organizer: 6th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications
  • Place of Presentation: ブダペスト, ハンガリー
  • Year and Date: 2009-05-09