Discrete convexity and polynomial solvability in minimum 0-extension problems

[1]  H. Hirai.  L-convexity on graph structures , 2016, 1610.02469.

[2]  Vladimir Kolmogorov,et al.  The Power of Linear Programming for General-Valued CSPs , 2013, SIAM J. Comput..

[3]  Shin-ichi Tanigawa,et al.  A Min-Max Theorem for Transversal Submodular Functions and Its Implications , 2014, SIAM J. Discret. Math..

[4]  Shin-ichi Tanigawa,et al.  Generalized skew bisubmodularity: A characterization and a min-max theorem , 2014, Discret. Optim..

[5]  Anna Huber,et al.  Oracle Tractability of Skew Bisubmodular Functions , 2013, SIAM J. Discret. Math..

[6]  Vladimir Kolmogorov,et al.  The Power of Linear Programming for Finite-Valued CSPs: A Constructive Characterization , 2013, ICALP.

[7]  Stanislav Zivny,et al.  The complexity of finite-valued CSPs , 2013, STOC '13.

[8]  Anna Huber,et al.  Skew Bisubmodularity and Valued CSPs , 2013, SIAM J. Comput..

[9]  Vladimir Kolmogorov,et al.  The complexity of conservative valued CSPs , 2011, JACM.

[10]  Hiroshi Hirai,et al.  Half-integrality of node-capacitated multiflows and tree-shaped facility locations on trees , 2010, Math. Program..

[11]  H. Hirai.  Discrete Convexity for Multiflows and 0-extensions , 2013 .

[12]  Stanislav Zivny,et al.  The Complexity of Valued Constraint Satisfaction Problems , 2012, Cognitive Technologies.

[13]  Anna Huber,et al.  Towards Minimizing k-Submodular Functions , 2012, ISCO.

[14]  Stanislav Zivny,et al.  The Power of Linear Programming for Valued CSPs , 2012, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science.

[15]  Hiroshi Hirai,et al.  Folder Complexes and Multiflow Combinatorial Dualities , 2011, SIAM J. Discret. Math..

[16]  Vladimir Kolmogorov,et al.  Submodularity on a Tree: Unifying $L^\natural$ -Convex and Bisubmodular Functions , 2010, MFCS.

[17]  Fredrik Kuivinen,et al.  On the complexity of submodular function minimisation on diamonds , 2009, Discret. Optim..

[18]  Hiroshi Hirai,et al.  The maximum multiflow problems with bounded fractionality , 2010, STOC '10.

[19]  Martin E. Dyer,et al.  On the complexity of #CSP , 2010, STOC '10.

[20]  Vladimir Kolmogorov,et al.  New algorithms for convex cost tension problem with application to computer vision , 2009, Discret. Optim..

[21]  Hiroshi Hirai,et al.  Tight spans of distances and the dual fractionality of undirected multiflow problems , 2009, J. Comb. Theory, Ser. B.

[22]  H. Bandelt,et al.  Metric graph theory and geometry: a survey , 2006 .

[23]  Alexander V. Karzanov.  Hard cases of the multifacility location problem , 2004, Discret. Appl. Math..

[24]  Kazuo Murota,et al.  Proximity theorems of discrete convex functions , 2004, Math. Program..

[25]  Alexander V. Karzanov.  One more well-solved case of the multifacility location problem , 2004, Discret. Optim..

[26]  Satoru Iwata,et al.  A combinatorial strongly polynomial algorithm for minimizing submodular functions , 2001, JACM.

[27]  Alexander Schrijver,et al.  A Combinatorial Algorithm Minimizing Submodular Functions in Strongly Polynomial Time , 2000, J. Comb. Theory B.

[28]  Hans-Jürgen Bandelt,et al.  A Characterization of Minimizable Metrics in the Multifacility Location Problem , 2000, Eur. J. Comb..

[29]  Kazuo Murota,et al.  Notes on L-/M-convex functions and the separation theorems , 2000, Math. Program..

[30]  Victor Chepoi,et al.  Graphs of Some CAT(0) Complexes , 2000, Adv. Appl. Math..

[31]  Kazuo Murota,et al.  Algorithms in discrete convex analysis , 2000 .

[32]  Éva Tardos,et al.  Approximation algorithms for classification problems with pairwise relationships: metric labeling and Markov random fields , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[33]  M. Bridson,et al.  Metric Spaces of Non-Positive Curvature , 1999 .

[34]  Kazuo Murota,et al.  M-Convex Function on Generalized Polymatroid , 1999, Math. Oper. Res..

[35]  Alexander V. Karzanov,et al.  Metrics with finite sets of primitive extensions , 1998 .

[36]  Alexander V. Karzanov,et al.  Minimum 0-Extensions of Graph Metrics , 1998, Eur. J. Comb..

[37]  Kazuo Murota,et al.  Discrete convex analysis , 1998, Math. Program..

[38]  André Bouchet,et al.  Multimatroids I. Coverings by Independent Sets , 1997, SIAM J. Discret. Math..

[39]  Francesca Rossi,et al.  Semiring-based constraint satisfaction and optimization , 1997, JACM.

[40]  Victor Chepoi,et al.  A Multifacility Location Problem on Median Spaces , 1996, Discret. Appl. Math..

[41]  Thomas Schiex,et al.  Valued Constraint Satisfaction Problems: Hard and Easy Problems , 1995, IJCAI.

[42]  Mihalis Yannakakis,et al.  The Complexity of Multiterminal Cuts , 1994, SIAM J. Comput..

[43]  Eric R. Verheul,et al.  Modular Interval Spaces , 1993 .

[44]  Tōkyō Daigaku.  Scientific papers of the College of Arts and Sciences, the University of Tokyo , 1993 .

[45]  Van de M. L. J. Vel.  Theory of convex structures , 1993 .

[46]  Dominique Peeters,et al.  Location on networks , 1992 .

[47]  藤重 悟.  Submodular functions and optimization , 1991 .

[48]  A. V. Karzanov.  Polyhedra related to undirected multicommodity flows , 1989 .

[49]  J. G. Pierce,et al.  Geometric Algorithms and Combinatorial Optimization , 2016 .

[50]  Liqun Qi,et al.  Directed submodularity, ditroids and directed submodular flows , 1988, Math. Program..

[51]  H. -J. Bandelt.  Hereditary modular graphs , 1988, Comb..

[52]  Ramaswamy Chandrasekaran,et al.  Pseudomatroids , 1988, Discret. Math..

[53]  Andreas W. M. Dress,et al.  Gated sets in metric spaces , 1987 .

[54]  Antoon Kolen,et al.  Tree network and planar rectilinear location theory , 1986 .

[55]  H. Bandelt.  Networks with condorcet solutions , 1985 .

[56]  R. L. Francis,et al.  State of the Art-Location on Networks: A Survey. Part II: Exploiting Tree Network Structure , 1983 .

[57]  Martin Grötschel,et al.  Mathematical Programming The State of the Art, XIth International Symposium on Mathematical Programming, Bonn, Germany, August 23-27, 1982 , 1983, ISMP.

[58]  László Lovász,et al.  Submodular functions and convexity , 1982, ISMP.

[59]  H. D. Ratliff,et al.  A Cut Approach to the Rectilinear Distance Facility Location Problem , 1978, Oper. Res..