Cross-Sectional Research of Discrete Convex Analysis

• Project/Area Number: 26280004
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Mathematical informatics
• Research Institution: Tokyo Metropolitan University (2015-2019); The University of Tokyo (2014)
• Principal Investigator: 室田 一雄 首都大学東京, 経営学研究科, 教授 (50134466)
• Project Period (FY): 2014-04-01 – 2020-03-31
• Project Status: Completed (Fiscal Year 2019)
• Budget Amount: ¥13,910,000 (Direct Cost: ¥10,700,000、Indirect Cost: ¥3,210,000); Fiscal Year 2018: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000); Fiscal Year 2017: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000); Fiscal Year 2016: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2015: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000); Fiscal Year 2014: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
• Keywords: 離散凸解析 / 最適化理論 / 数理工学 / 情報基盤 / アルゴリズム / 経済理論 / 情報基礎

Outline of Annual Research Achievements

諸分野における共通の方法論としての離散凸解析を発展させるべく，以下の成果を得た．
昨年度までの研究で整凸関数の近接定理や最小化アルゴリズムが解明されたことを踏まえ，従来より離散凸解析において中心的な役割を果たしてきたＬ#(natural)凸関数との関係をより明確にすべきであるとの認識を得た．そこで，イタリア人研究者をふくむ研究協力者らとともに，Ｌ#凸関数を特徴づける離散中点凸性の一般化を探求した結果，離散中点凸関数という概念に至り，これに対してＬ#凸関数の近接定理が同じ形のままで拡張できることなどを示し，さらにそれを用いたアルゴリズムを開発した．
離散凸関数に対する射影，制限，合成積，集約，分離，ネットワーク変換などの基本演算を網羅的に解明した．その結果，ジャンプシステム上のＭ凸関数，マルチモジュラ関数，整凸関数，離散中点凸関数までを含む離散凸関数の主なクラスについて，その基本演算の可否を一覧表の形に整理することができた．
離散資源の公平配分に関する研究をハンガリー人研究者とともに強力に推進し，Ｍ凸集合上の辞書式最適化および整数値ネットワーク流の辞書式最適化に関して，基本的かつ重要な成果を得た．その一部を国内外の研究集会において発表した．本研究で得られた成果とアプローチは，オペレーションズ・リサーチにおける離散資源配分問題，コンピュータ科学における計算資源の割当問題，グラフ理論における向き付け問題，ゲーム理論における平等主義的配分など，多くの応用を有するものである．

Research Progress Status

令和元年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

令和元年度が最終年度であるため、記入しない。

Research Products

• [Int'l Joint Research] Eotvos University(ハンガリー)
  • Country Name: ハンガリー
  • Counterpart Institution: Eotvos University
• [Int'l Joint Research] University of Oxford(英国)
  • Country Name: 英国
  • Counterpart Institution: University of Oxford
• [Int'l Joint Research] Sapienza University of Rome(イタリア)
  • Country Name: イタリア
  • Counterpart Institution: Sapienza University of Rome
• [Int'l Joint Research] University of British Columbia(カナダ)
  • Country Name: カナダ
  • Counterpart Institution: University of British Columbia
• [Int'l Joint Research] Sapienza University of Rome(イタリア)
  • Country Name: イタリア
  • Counterpart Institution: Sapienza University of Rome
• [Int'l Joint Research] University of Oxford(イギリス)
  • Country Name: イギリス
  • Counterpart Institution: University of Oxford
• [Int'l Joint Research] Sapienza University of Rome(イタリア)
  • Country Name: イタリア
  • Counterpart Institution: Sapienza University of Rome
• [Journal Article] Integrality of subgradients and biconjugates of integrally convex functions (2020)
  • Author(s): K. Murota, A. Tamura
  • Journal Title: Optimization Letters Volume: 14 Pages: 195-208
  • DOI: 10.1007/s11590-019-01501-1
  • Peer Reviewed
• [Journal Article] Discrete midpoint convexity (2020)
  • Author(s): S. Moriguchi, K. Murota, A. Tamura, F. Tardella
  • Journal Title: Mathematics of Operations Research Volume: 45 Pages: 99-128
  • DOI: 10.1287/moor.2018.0984
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] A survey of fundamental operations on discrete convex functions of various kinds (2020)
  • Author(s): K. Murota
  • Journal Title: Optimization Methods and Software Volume: - Pages: -
  • DOI: 10.1080/10556788.2019.1692345
  • Peer Reviewed
• [Journal Article] Projection and convolution operations for integrally convex functions (2019)
  • Author(s): S. Moriguchi, K. Murota
  • Journal Title: Discrete Applied Mathematics Volume: 255 Pages: 283-298
  • DOI: 10.1016/j.dam.2018.08.010
  • Peer Reviewed
• [Journal Article] Error noted in ``Order-Based Cost Optimization in Assemble-to-Order Systems'' by Lu and Song (2005) (2019)
  • Author(s): M. Bolandnazar, W. T. Huh, S. T. McCormick, K. Murota
  • Journal Title: Operations Research Volume: 67 Pages: 163-166
  • DOI: 10.1287/opre.2018.1789
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] On fundamental operations for multimodular functions (2019)
  • Author(s): S. Moriguchi, K. Murota
  • Journal Title: Journal of the Operations Research Society of Japan Volume: 62 Pages: 53-63
  • Peer Reviewed / Open Access
• [Journal Article] Scaling, proximity, and optimization of integrally convex functions (2019)
  • Author(s): S. Moriguchi, K. Murota, A. Tamura, F. Tardella
  • Journal Title: Mathematical Programming Volume: 175 Pages: 119-154
  • DOI: 10.1007/s10107-018-1234-z
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] A tractable class of binary VCSPs via M-convex intersection (2019)
  • Author(s): H. Hirai, Y. Iwamasa, K. Murota, S. Zivny
  • Journal Title: ACM Transactions on Algorithms Volume: 15 Pages: Article 44
  • DOI: doi.org/10.1145/3329862
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] On fundamental operations for multimodular functions (2019)
  • Author(s): S. Moriguchi and K. Murota
  • Journal Title: Journal of the Operations Research Society of Japan Volume: 62 Pages: 印刷中
  • Peer Reviewed
• [Journal Article] Integrality of subgradients and biconjugates of integrally convex functions (2019)
  • Author(s): K. Murota and A. Tamura
  • Journal Title: Optimization Letters Volume: 13 Pages: 印刷中
  • Peer Reviewed
• [Journal Article] Discrete midpoint convexity (2019)
  • Author(s): S. Moriguchi, K. Murota, A. Tamura, F. Tardella
  • Journal Title: Mathematics of Operations Research Volume: 45 Pages: 印刷中
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Multiple Exchange Property for M#-Concave Functions and Valuated Matroids (2018)
  • Author(s): K. Murota
  • Journal Title: Mathematics of Operations Research Volume: 43 Pages: 781～788
  • DOI: https://doi.org/10.1287/moor.2017.0882
  • Peer Reviewed
• [Journal Article] Continuous relaxation for discrete DC programming (2018)
  • Author(s): T. Maehara, N. Marumo, K. Murota
  • Journal Title: Mathematical Programming Volume: 169 Pages: 199～219
  • DOI: 10.1007/s10107-017-1139-2
  • Peer Reviewed
• [Journal Article] Discrete convexity in joint winner property (2018)
  • Author(s): Y. Iwamasa, K. Murota, S. Zivny
  • Journal Title: Discrete Optimization Volume: 28 Pages: 78～88
  • DOI: https://doi.org/10.1016/j.disopt.2018.01.001
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] On equivalence of M-natural-concavity of a set function and submodularity of its conjugate (2018)
  • Author(s): K. Murota, A. Shioura
  • Journal Title: Journal of the Operations Research Society of Japan Volume: 61 Pages: 163-171
  • Peer Reviewed
• [Journal Article] Simpler exchange axioms for M-concave functions on generalized polymatroids (2018)
  • Author(s): Murota Kazuo、Shioura Akiyoshi
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 35 Pages: 235～259
  • DOI: 10.1007/s13160-017-0285-5
  • Peer Reviewed
• [Journal Article] A stronger multiple exchange property for M-natural-concave functions (2018)
  • Author(s): Murota Kazuo
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 35 Pages: 411～421
  • DOI: 10.1007/s13160-017-0278-4
  • Peer Reviewed
• [Journal Article] Beyond JWP: A tractable class of binary VCSPs via M-convex intersection (2018)
  • Author(s): Hirai Hiroshi、Iwamasa Yuni、Murota Kazuo、Zivny Stanislav
  • Journal Title: Proceedings of the 35th International Symposium on Theoretical Aspects of Computer Science (STACS'18), LIPIcs Volume: 96 Pages: 39:1～39:14
  • DOI: 10.4230/LIPIcs.STACS.2018.39
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Note on time bounds of two-phase algorithms for L-convex function minimization (2017)
  • Author(s): Murota Kazuo、Shioura Akiyoshi
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 34 Pages: 429～440
  • DOI: 10.1007/s13160-017-0246-z
  • Peer Reviewed
• [Journal Article] Multiple Exchange Property for M-natural-Concave Functions and Valuated Matroids (2017)
  • Author(s): Murota Kazuo
  • Journal Title: Mathematics of Operations Research Volume: 印刷中 Pages: 印刷中
  • DOI: 10.1287/moor.2017.0882
  • Peer Reviewed
• [Journal Article] 学生にグループ分けのある学科配属問題― 離散凸解析の適用例 (2017)
  • Author(s): 赤堀峻、 関口陽介、 田村 明久
  • Journal Title: Transactions of the Operations Research Society of Japan Volume: 60 Pages: 50～73
  • DOI: 10.15807/torsj.60.50
  • Peer Reviewed
• [Journal Article] Discrete convex analysis: A tool for economics and game theory (2016)
  • Author(s): K. Murota
  • Journal Title: Journal of Mechanism and Institution Design Volume: 1 Pages: 151-273
  • DOI: 10.22574/jmid.2016.12.005
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Scaling and proximity properties of integrally convex functions (2016)
  • Author(s): S. Moriguchi, K. Murota, A. Tamura, and F. Tardella
  • Journal Title: 27th International Symposium on Algorithms and Computation (ISAAC 2016), Seok-Hee Hong (Ed.): ISAAC2016, Leibniz International Proceedings in Informatics (LIPIcs) Volume: 64 Pages: 57:1-57:12
  • DOI: 10.4230/LIPIcs.ISAAC.2016.0
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Extended formulations for sparsity matroids (2016)
  • Author(s): S. Iwata, N. Kamiyama, N. Katoh, S. Kijima, and Y. Okamoto
  • Journal Title: Mathematical Programming, Series A Volume: 158 Pages: 565-574
  • DOI: 10.1007/s10107-015-0936-8
  • Peer Reviewed
• [Journal Article] Covering intersecting bi-set families under matroid constraints (2016)
  • Author(s): K. Berczi, T. Kiraly, and Y. Kobayashi
  • Journal Title: SIAM Journal on Discrete Mathematics Volume: 30 Pages: 1758-1774
  • DOI: 10.1137/15M1049099
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Improved max-flow min-cut algorithms in a circular disk failure model with application to a road network (2016)
  • Author(s): K. Otsuki, Y. Kobayashi, and K. Murota
  • Journal Title: European Journal of Operational Research Volume: 248 Pages: 396-403
  • DOI: 10.1016/j.ejor.2015.07.035
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Finding a stable allocation in polymatroid intersection (2016)
  • Author(s): S. Iwata and Y. Yokoi
  • Journal Title: Proceedings of the 27th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2016) Volume: なし Pages: 1034-1047
  • DOI: 10.1137/1.9781611974331.ch73
  • Peer Reviewed
• [Journal Article] Improved approximation algorithms for k-submodular function maximization (2016)
  • Author(s): S. Iwata, S. Tanigawa, Y. Yoshida
  • Journal Title: Proceedings of the 27th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2016) Volume: なし Pages: 404-413
  • DOI: 10.1137/1.9781611974331.ch30
  • Peer Reviewed
• [Journal Article] Application of submodular optimization to single machine scheduling with controllable processing times subject to release dates and deadlines (2016)
  • Author(s): A. Shioura, N. V. Shakhlevich, and V. A. Strusevich
  • Journal Title: INFORMS Journal on Computing Volume: 28 Pages: 148-161
  • DOI: 10.1287/ijoc.2015.0660
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Time bounds for iterative auctions: a unified approach by discrete convex analysis (2016)
  • Author(s): K. Murota, A. Shioura, and Z. Yang
  • Journal Title: Discrete Optimization Volume: 19 Pages: 36-62
  • DOI: 10.1016/j.disopt.2016.01.001
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Stability in supply chain networks: An approach by discrete convex analysis (2015)
  • Author(s): Y. T Ikebe and A. Tamura
  • Journal Title: Journal of the Operations Research Society of Japan Volume: 58 Pages: 271-290
  • Peer Reviewed / Open Access
• [Journal Article] Stability and competitive equilibria in multi-unit trading networks with discrete concave utility functions (2015)
  • Author(s): Y. T Ikebe, Y. Sekiguchi, A. Shioura and A. Tamura
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 32 Pages: 373-410
  • DOI: 10.1007/s13160-015-0175-7
  • Peer Reviewed
• [Journal Article] The complexity of minimizing the difference of two M-natural convex set functions (2015)
  • Author(s): Y. Kobayashi
  • Journal Title: Operations Research Letters Volume: 43 Pages: 573-574
  • DOI: 10.1016/j.orl.2015.08.011
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Equilibrium, auction, and generalized gross substitutes and complements (2015)
  • Author(s): A. Shioura and Z. Yang
  • Journal Title: Journal of Operations Research Society of Japan Volume: 58 Pages: 410-435
  • DOI: 10.15807/jorsj.58.410
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Monotonicity in steepest ascent algorithms for polyhedral L-concave functions (2015)
  • Author(s): S. Fujishige, K. Murota, and A. Shioura
  • Journal Title: Journal of Operations Research Society of Japan Volume: 58 Pages: 184-208
  • DOI: 10.15807/jorsj.58.184
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Valuated matroid-based algorithm for submodular welfare problem (2015)
  • Author(s): T. Maehara and K. Murota
  • Journal Title: Annals of Operations Research Volume: 229 Pages: 565-590
  • DOI: 10.1007/s10479-015-1835-3
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] On polyhedral approximation of L-convex and M-convex functions (2015)
  • Author(s): K. Murota
  • Journal Title: Journal of the Operations Research Society of Japan Volume: 58 Pages: 291-305
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Continuous relaxation for discrete DC programming (2015)
  • Author(s): T. Maehara, N. Marumo, and K. Murota
  • Journal Title: Advances in Intelligent Systems and Computing Volume: 359 Pages: 181-190
  • DOI: 10.1007/878-3-319-18161-5_16
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Monotonicity in steepest ascent algorithms for polyhedral L-concave functions (2015)
  • Author(s): S. Fujishige, K. Murota and A. Shioura
  • Journal Title: Journal of Operations Research Society of Japan Volume: 58 Pages: 印刷中
  • Peer Reviewed / Open Access
• [Journal Article] On the lattice structure of stable allocations in two-sided discrete-concave market (2015)
  • Author(s): K. Murota and Y. Yokoi
  • Journal Title: Mathematics of Operations Research Volume: 40 Pages: 460-473
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Gross substitutes condition and discrete concavity for multi-unit valuations: A survey (2015)
  • Author(s): A. Shioura, A. Tamura
  • Journal Title: Journal of the Operations Research Society of Japan Volume: 58 Pages: 61-103
  • Peer Reviewed / Open Access
• [Journal Article] Stability in supply chain networks: An approach by discrete convex analysis (2015)
  • Author(s): Y.T. Ikebe, A. Tamura
  • Journal Title: Journal of the Operations Research Society of Japan Volume: 58 Pages: 印刷中
  • Peer Reviewed / Open Access
• [Journal Article] Polynomial-time approximation schemes for maximizing gross substitutes utility under budget constraints (2015)
  • Author(s): A. Shioura
  • Journal Title: Mathematics of Operations Research Volume: 40 (1) Pages: 171-191
  • DOI: 10.1287/moor.2014.0668
  • Peer Reviewed
• [Journal Article] A framework of discrete DC programming by discrete convex analysis (2014)
  • Author(s): T. Maehara and K. Murota
  • Journal Title: Mathematical Programming, Series A Volume: ― Pages: ―
  • DOI: 10.1007/s10107-014-0792-y
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Decomposition algorithms for submodular optimization with applications to parallel machine scheduling with controllable processing times (2014)
  • Author(s): A. Shioura, N. V. Shakhlevich, and V. A. Strusevich
  • Journal Title: Mathematical Programming Volume: 印刷中 Pages: 印刷中
  • DOI: 10.1007/s10107-014-0814-9
  • Peer Reviewed
• [Journal Article] A unified view to greedy geometric routing algorithms in ad hoc networks (2014)
  • Author(s): J. Chun, A. Shioura, T. M. Tien, and T. Tokuyama
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E97-A (6) Pages: 1220-1230
  • Peer Reviewed
• [Journal Article] Triangle-free 2-matchings and M-concave functions on jump systems (2014)
  • Author(s): Y. Kobayashi
  • Journal Title: Discrete Applied Mathematics Volume: 175 Pages: 35-42
  • DOI: 10.1016/j.dam.2014.05.016
  • Peer Reviewed
• [Presentation] Discrete convex analysis view on discrete decreasing minimization (2019)
  • Author(s): A. Frank, K. Murota
  • Organizer: The 11th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications
  • Int'l Joint Research
• [Presentation] Discrete convex analysis for egalitarian allocation (2019)
  • Author(s): K. Murota
  • Organizer: NACA-ICOTA2019
  • Int'l Joint Research / Invited
• [Presentation] Discrete decreasingly minimal flows (2019)
  • Author(s): A. Frank, K. Murota
  • Organizer: 日本オペレーションズ・リサーチ学会2019年秋季研究発表会
• [Presentation] 離散凸関数の最大最小定理：その具体例と使い方 (2019)
  • Author(s): 室田一雄
  • Organizer: 「離散凸解析と最適化」ワークショップ
  • Invited
• [Presentation] Scaling, proximity, and optimization of integrally convex functions (2018)
  • Author(s): S. Moriguchi, A. Tamura, F. Tardella, K. Murota
  • Organizer: 23rd International Symposium on Mathematical Programming
  • Int'l Joint Research
• [Presentation] Discrete midpoint convexity (2018)
  • Author(s): F. Tardella, K. Murota, A. Tamura, S. Moriguchi
  • Organizer: 23rd International Symposium on Mathematical Programming
  • Int'l Joint Research
• [Presentation] Discrete convexity in binary VCSPs (2018)
  • Author(s): H. Hirai, Y. Iwamasa, K. Murota, S. Zivny
  • Organizer: 23rd International Symposium on Mathematical Programming
  • Int'l Joint Research
• [Presentation] Discrete DC programming for integrally convex functions, (2018)
  • Author(s): K. Murota
  • Organizer: Discrete Optimization and Machine Learning (Riken AIP)
  • Int'l Joint Research / Invited
• [Presentation] 離散凸解析 ― 最近の進展を中心に (2018)
  • Author(s): 室田一雄
  • Organizer: RIMS 共同研究「組合せ最適化セミナー(第15回)
  • Invited
• [Presentation] 整凸関数の劣勾配と双共役関数の整数性 (2018)
  • Author(s): 室田一雄，田村明久
  • Organizer: 日本オペレーションズ・リサーチ学会2018年秋季研究発表会
• [Presentation] マルチモジュラ関数の基本演算について (2018)
  • Author(s): 森口聡子，室田一雄
  • Organizer: 日本オペレーションズ・リサーチ学会2018年秋季研究発表会
• [Presentation] DC Programming in Discrete Convex Analysis (2018)
  • Author(s): K. Murota
  • Organizer: The 6th Asian Conference on Nonlinear Analysis and Optimization
  • Int'l Joint Research / Invited
• [Presentation] 整凸関数の離散凸解析における役割 (2018)
  • Author(s): 室田一雄
  • Organizer: 日本オペレーションズ・リサーチ学会「離散アルゴリズムの応用と理論」研究部会
  • Invited
• [Presentation] Algorithms for discrete midpoint convex functions (2018)
  • Author(s): S. Moriguchi, K. Murota, A. Tamura, and F. Tardella
  • Organizer: 最適化：モデリングとアルゴリズム
• [Presentation] Multiple exchange property of M-concave functions (2017)
  • Author(s): K. Murota
  • Organizer: 日本オペレーションズ・リサーチ学会2017年春季研究発表会
  • Place of Presentation: 沖縄県市町村自治会館（沖縄県那覇市）
  • Year and Date: 2017-03-15 – 2017-03-17
• [Presentation] 整凸関数の基本演算について (2017)
  • Author(s): 森口聡子，室田一雄
  • Organizer: 日本オペレーションズ・リサーチ学会2017年春季研究発表会
  • Place of Presentation: 沖縄県市町村自治会館（沖縄県那覇市）
  • Year and Date: 2017-03-15 – 2017-03-17
• [Presentation] 複数財に対する繰り返しオークションと離散凸解析の繋がり (2017)
  • Author(s): 塩浦昭義
  • Organizer: 日本オペレーションズ・リサーチ学会関西支部記念講演会
  • Place of Presentation: 関西大学うめきたラボラトリ（大阪市北区）
  • Year and Date: 2017-03-11
  • Invited
• [Presentation] Multiple exchange in M#-concave functions and its implication in economics (2017)
  • Author(s): K. Murota
  • Organizer: The 10th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications
  • Int'l Joint Research
• [Presentation] Time bounds of two-phase algorithms for L-convex function minimization (2017)
  • Author(s): K. Murota and A. Shioura
  • Organizer: The 10th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications
  • Int'l Joint Research
• [Presentation] Discrete convexity in joint winner property (2017)
  • Author(s): Y. Iwamasa, K. Murota, and S. Zivny
  • Organizer: 19th Conference on Integer Programming and Combinatorial Optimization
  • Int'l Joint Research
• [Presentation] Discrete convexity in valued constraint satisfaction problems: Joint winner property and M-convexity (2017)
  • Author(s): Y. Iwamasa, K. Murota, and S. Zivny
  • Organizer: 離散数学とその応用研究集会2017
• [Presentation] Discrete convexity in joint winner property (2017)
  • Author(s): Y. Iwamasa, K. Murota, and S. Zivny
  • Organizer: 日本応用数理学会2017年度年会
• [Presentation] M#凹集合関数の多重交換公理の精密化 (2017)
  • Author(s): K. Murota
  • Organizer: 日本オペレーションズ・リサーチ学会2017年秋季研究発表会
• [Presentation] Discrete Midpoint Convexity (2017)
  • Author(s): S. Moriguchi, K. Murota, A. Tamura, and F. Tardella
  • Organizer: 日本オペレーションズ・リサーチ学会2017年秋季研究発表会
• [Presentation] On discrete midpoint convexity (2017)
  • Author(s): K. Murota
  • Organizer: Franco-Japanese Days on Combinatorics and Optmization 2017
  • Int'l Joint Research / Invited
• [Presentation] Scaling and proximity properties of integrally convex functions (2016)
  • Author(s): S. Moriguchi, K. Murota, A. Tamura, and F. Tardella
  • Organizer: 27th International Symposium on Algorithms and Computation (ISAAC 2016)
  • Place of Presentation: シドニー（オーストラリア）
  • Year and Date: 2016-12-12 – 2016-12-14
  • Int'l Joint Research
• [Presentation] グラフ上の離散凸関数について (2016)
  • Author(s): 平井広志
  • Organizer: 日本OR学会九州支部平成28年度第３回講演会・研究会
  • Place of Presentation: 西南学院大学（福岡県福岡市）
  • Year and Date: 2016-12-10
  • Invited
• [Presentation] 離散凸解析とオークション理論の接点 (2016)
  • Author(s): 室田一雄
  • Organizer: 武蔵野大学 2016年度 数理工学シンポジウム
  • Place of Presentation: 武蔵野大学有明キャンパス（東京都江東区）
  • Year and Date: 2016-11-21 – 2016-11-22
  • Invited
• [Presentation] Directed integrally convex functions (2016)
  • Author(s): S. Moriguchi, K. Murota, A. Tamura, and F. Tardella
  • Organizer: 日本オペレーションズ・リサーチ学会2016年秋季研究発表会
  • Place of Presentation: 山形大学（山形県山形市）
  • Year and Date: 2016-09-15 – 2016-09-16
• [Presentation] Convex analysis approach to discrete optimization (2016)
  • Author(s): K. Murota
  • Organizer: Summer school of ICCOPT 2016 (The fifth International Conference on Continuous Optimization)
  • Place of Presentation: オリンピック記念青少年総合センター（東京都渋谷区）
  • Year and Date: 2016-08-07
  • Int'l Joint Research / Invited
• [Presentation] Discrete Convex Analysis III: Algorithms for discrete convex functions (2016)
  • Author(s): K. Murota
  • Organizer: Hausdorff School: Economics and Tropical Geometry
  • Place of Presentation: ボン（ドイツ）
  • Year and Date: 2016-05-12
  • Int'l Joint Research / Invited
• [Presentation] Discrete Convex Analysis II: Properties of discrete convex functions (2016)
  • Author(s): K. Murota
  • Organizer: Hausdorff School: Economics and Tropical Geometry
  • Place of Presentation: ボン（ドイツ）
  • Year and Date: 2016-05-10
  • Int'l Joint Research / Invited
• [Presentation] Discrete Convex Analysis I: Concepts of discrete convex functions (2016)
  • Author(s): K. Murota
  • Organizer: Hausdorff School: Economics and Tropical Geometry
  • Place of Presentation: ボン（ドイツ）
  • Year and Date: 2016-05-09
  • Int'l Joint Research / Invited
• [Presentation] 離散凸解析をひろげる (2016)
  • Author(s): 塩浦昭義
  • Organizer: 日本オペレーションズ・リサーチ学会2016年春季研究発表会
  • Place of Presentation: 慶應義塾大学（神奈川県横浜市）
  • Year and Date: 2016-03-18
  • Invited
• [Presentation] Scaling and Proximity Properties of Integrally Convex Functions (2016)
  • Author(s): S. Moriguchi, K. Murota, and F. Tardella
  • Organizer: 日本オペレーションズ・リサーチ学会2016年春季研究発表会
  • Place of Presentation: 慶應義塾大学 (神奈川県横浜市)
  • Year and Date: 2016-03-18
• [Presentation] 双有向森問題に対する二つの双対定理の関係 (2016)
  • Author(s): 室田 一雄，高澤兼二郎
  • Organizer: 日本オペレーションズ・リサーチ学会2016年春季研究発表会
  • Place of Presentation: 慶應義塾大学 (神奈川県横浜市)
  • Year and Date: 2016-03-18
• [Presentation] L凸関数の最小化アルゴリズム:離散凸解析と諸分野との繋がり (2015)
  • Author(s): 塩浦昭義
  • Organizer: 第27回RAMPシンポジウム
  • Place of Presentation: 静岡大学浜松キャンパス（静岡県浜松市）
  • Year and Date: 2015-10-15
  • Invited
• [Presentation] Analysis of L-convex Function Minimization Algorithms and Application to Auction Theory (2015)
  • Author(s): Akiyoshi Shioura
  • Organizer: Hausdorff Research Institute for Mathematics , Trimester Program, Combinatorial Optimization, Workshop on Rigidity, Submodularity, Discrete Convexity
  • Place of Presentation: ボン (ドイツ)
  • Year and Date: 2015-10-06
  • Int'l Joint Research
• [Presentation] Extensions and ramifications of discrete convexity concepts (2015)
  • Author(s): K. Murota
  • Organizer: Hausdorff Institute of Mathematics, Trimester Program, Combinatorial Optimization, Workshop on Rigidity, Submodularity, Discrete Convexity
  • Place of Presentation: ボン（ドイツ）
  • Year and Date: 2015-10-06
  • Int'l Joint Research / Invited
• [Presentation] Discrete convex analysis (2015)
  • Author(s): K. Murota
  • Organizer: Hausdorff Institute of Mathematics, Trimester Program, Combinatorial Optimization, Summer School on Combinatorial Optimization
  • Place of Presentation: ボン（ドイツ）
  • Year and Date: 2015-09-21 – 2015-09-25
  • Int'l Joint Research / Invited
• [Presentation] Exact Bounds for Steepest Descent Algorithms of L-convex Function Minimization (2015)
  • Author(s): Akiyoshi Shioura
  • Organizer: 22nd International Symposium on Mathematical Programming
  • Place of Presentation: ピッツバーグ（米国）
  • Year and Date: 2015-07-17
  • Int'l Joint Research
• [Presentation] Multi-unit trading networks with discrete concave utility functions (2015)
  • Author(s): Y. T Ikebe, Y. Sekiguchi, A. Shioura and A. Tamura
  • Organizer: 22nd International Symposium on Mathematical Programming
  • Place of Presentation: ピッツバーグ（米国）
  • Year and Date: 2015-07-16
  • Int'l Joint Research
• [Presentation] On polyhedral approximation of L-convex and M-convex functions (2015)
  • Author(s): K. Murota
  • Organizer: 22nd International Symposium on Mathematical Programming
  • Place of Presentation: ピッツバーグ（米国）
  • Year and Date: 2015-07-15
  • Int'l Joint Research
• [Presentation] Multi-unit trading networks with discrete concave utility functions (2015)
  • Author(s): Y. T Ikebe, Y. Sekiguchi, A. Shioura and A. Tamura
  • Organizer: The 9th Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications
  • Place of Presentation: 九州大学西新プラザ（福岡県福岡市）
  • Year and Date: 2015-06-03
  • Int'l Joint Research
• [Presentation] On k-Submodular Relaxation (2015)
  • Author(s): Hiroshi Hirai and Yuni Iwamasa
  • Organizer: The 9th Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications
  • Place of Presentation: 九州大学西新プラザ（福岡県福岡市）
  • Year and Date: 2015-06-02
  • Int'l Joint Research
• [Presentation] Continuous relaxation for discrete DC programming (2015)
  • Author(s): T. Maehara, N. Marumo, and K. Murota
  • Organizer: 3rd International Conference on Modelling, Computation and Optimization in Information Systems and Management Sciences -- MCO 2015
  • Place of Presentation: メス (フランス)
  • Year and Date: 2015-05-12
  • Int'l Joint Research
• [Presentation] 有向木詰め込みに関する最大最小定理 (2015)
  • Author(s): 小林佑輔
  • Organizer: 日本オペレーションズ・リサーチ学会「最適化の基盤とフロンティア」研究部会（WOO）
  • Place of Presentation: 東京理科大学（東京都新宿区）
  • Year and Date: 2015-03-28
  • Invited
• [Presentation] 歪M-natural 凹関数を用いた取引ネットワークモデル (2015)
  • Author(s): 池辺淑子, 関口陽介, 塩浦昭義, 田村明久
  • Organizer: 日本オペレーションズリサーチ学会春季研究発表会
  • Place of Presentation: 東京理科大学（東京都新宿区）
  • Year and Date: 2015-03-27
• [Presentation] 離散DC計画問題に対する連続緩和 (2015)
  • Author(s): 前原貴憲，丸茂直貴，室田一雄
  • Organizer: 日本オペレーションズ・リサーチ学会2015年春季研究発表会
  • Place of Presentation: 東京理科大学（東京都新宿区）
  • Year and Date: 2015-03-26
• [Presentation] 離散凸性判定プログラムの実装 (2015)
  • Author(s): 土村展之，森口聡子，室田一雄
  • Organizer: 日本オペレーションズ・リサーチ学会2015年春季研究発表会
  • Place of Presentation: 東京理科大学（東京都新宿区）
  • Year and Date: 2015-03-26
• [Presentation] Speed scaling scheduling viewed from submodular optimization (2015)
  • Author(s): A. Shioura
  • Organizer: 応用数理学会研究部会連合発表会
  • Place of Presentation: 明治大学中野キャンパス(東京都中野区)
  • Year and Date: 2015-03-06
• [Presentation] DC programming in discrete convex analysis (2015)
  • Author(s): K. Murota
  • Organizer: IMA Workshop Convexity and Optimization: Theory and Applications
  • Place of Presentation: Institute for Mathematics and Its Applications (Minneapolis, USA)
  • Year and Date: 2015-02-23 – 2015-02-27
  • Invited
• [Presentation] Energy optimization in speed scaling models via submodular optimization (2014)
  • Author(s): A. Shioura
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 崇城大学（熊本県熊本市）
  • Year and Date: 2014-12-05
• [Presentation] Minimization of L-convex function and its application (2014)
  • Author(s): A. Shioura
  • Organizer: 2014 Bilateral Workshop between Tohoku University and National Tsing Hua University
  • Place of Presentation: ホテル松島大観荘（宮城県宮城郡松島町）
  • Year and Date: 2014-11-21
  • Invited
• [Presentation] 円板形領域損傷モデルにおける最大流最小カットアルゴリズム (2014)
  • Author(s): 大槻兼資，小林佑輔，室田一雄
  • Organizer: 日本オペレーションズ・リサーチ学会「公共的社会システムとOR」研究部会
  • Place of Presentation: 政策研究大学院大学（東京都港区）
  • Year and Date: 2014-11-17
• [Presentation] Discrete DC programming by discrete convex analysis (2014)
  • Author(s): K. Murota
  • Organizer: Oberwolfach Workshop on Combinatorial Optimization
  • Place of Presentation: Mathematisches Forschungsinstitut Oberwolfach (Oberwolfach, Germany)
  • Year and Date: 2014-11-11
  • Invited
• [Presentation] 混合多項式行列における小行列式最大次数列に対する組合せ緩和法 (2014)
  • Author(s): 佐藤 峻, 室田 一雄
  • Organizer: 日本応用数理学会2014年度年会
  • Place of Presentation: 政策研究大学院大学（東京都港区）
  • Year and Date: 2014-09-05
• [Presentation] 小行列式最大次数列に対する組合せ緩和法の効率化 (2014)
  • Author(s): 佐藤 峻，室田 一雄
  • Organizer: 日本オペレーションズ・リサーチ学会2014年秋季研究発表会
  • Place of Presentation: 北海道科学大学（北海道札幌市）
  • Year and Date: 2014-08-28
• [Presentation] Stability and competitive equilibrium in extended trading networks with discrete concave utility functions (2014)
  • Author(s): Y.T. Ikebe, Y. Sekiguchi, A. Shioura and A. Tamura
  • Organizer: The Second International Workshop on Market Design Technologies for Substainable Development
  • Place of Presentation: Keio University（横浜市港北区）
  • Year and Date: 2014-08-17
  • Invited
• [Presentation] Max-flow min-cut theorem and faster algorithms in a circular disk failure model (2014)
  • Author(s): 小林佑輔
  • Organizer: JST ERATO 河原林巨大グラフプロジェクト・感謝祭 Summer 2014
  • Place of Presentation: 国立情報学研究所（東京都港区）
  • Year and Date: 2014-08-08
• [Presentation] Computing a Walrasian equilibrium in iterative auctions with multiple differentiated items (2014)
  • Author(s): A. Shioura
  • Organizer: Japanese-Swiss Workshop on Combinatorics and Computational Geometry
  • Place of Presentation: 東京大学(東京都文京区）
  • Year and Date: 2014-06-05
  • Invited
• [Presentation] アルゴリズムの評価：安定結婚問題を通して (2014)
  • Author(s): 田村明久
  • Organizer: 日本オペレーションズリサーチ学会研究部会SOTA
  • Place of Presentation: 筑波大学（茨城県つくば市）
  • Year and Date: 2014-05-31
  • Invited
• [Presentation] Max-flow min-cut theorem and faster algorithms in a circular disk failure model (2014)
  • Author(s): Y. Kobayashi and K. Otsuki
  • Organizer: The 33rd Annual IEEE International Conference on Computer Communications (INFOCOM 2014)
  • Place of Presentation: Toronto, Canada
  • Year and Date: 2014-04-27 – 2014-05-02
• [Presentation] Auction theory and discrete convex analysis (2014)
  • Author(s): K. Murota
  • Organizer: Meeting in honor of Andras Sebo
  • Place of Presentation: University of Grenoble (Grenoble, France)
  • Year and Date: 2014-04-24 – 2014-04-25
  • Invited
• [Presentation] Time complexity analysis of iterative auctions with multiple differentiated items (2014)
  • Author(s): K. Murota and A. Shioura, and Z. Yang
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 東北大学（宮城県仙台市）
  • Year and Date: 2014-04-24
• [Presentation] Time complexity analysis of iterative auctions with multiple differentiated Items (2014)
  • Author(s): 塩浦昭義
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 東北大学（宮城県仙台市）
  • Year and Date: 2014-04-24
• [Remarks] DCP (Discrete Convex Paradigm)
  • URL: http://ist.ksc.kwansei.ac.jp/~tutimura/DCP/
• [Remarks] DCP (Discrete Convex Paradigm)
  • URL: http://www.misojiro.t.u-tokyo.ac.jp/DCP/