Academic literature on the topic 'Box-Totally dual integral polyhedron'
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Journal articles on the topic "Box-Totally dual integral polyhedron":
Cook, William. "On box totally dual integral polyhedra." Mathematical Programming 34, no. 1 (January 1986): 48–61. http://dx.doi.org/10.1007/bf01582162.
Chervet, Patrick, Roland Grappe, Mathieu Lacroix, Francesco Pisanu, and Roberto Wolfler Calvo. "Hard problems on box-totally dual integral polyhedra." Discrete Optimization 50 (November 2023): 100810. http://dx.doi.org/10.1016/j.disopt.2023.100810.
Ding, Guoli, Lei Tan, and Wenan Zang. "When Is the Matching Polytope Box-Totally Dual Integral?" Mathematics of Operations Research 43, no. 1 (February 2018): 64–99. http://dx.doi.org/10.1287/moor.2017.0852.
Frank, András, and Kazuo Murota. "A Discrete Convex Min-Max Formula for Box-TDI Polyhedra." Mathematics of Operations Research, October 18, 2021. http://dx.doi.org/10.1287/moor.2021.1160.
Chervet, Patrick, Roland Grappe, Francesco Pisanu, Mathieu Lacroix, and Calvo Roberto Wolfler. "Hard Problems on Box-Totally Dual Integral Polyhedra." SSRN Electronic Journal, 2023. http://dx.doi.org/10.2139/ssrn.4397713.
Kerivin, Hervé L. M., and Jinhua Zhao. "Bounded-degree rooted tree and TDI-ness." RAIRO - Operations Research, June 16, 2022. http://dx.doi.org/10.1051/ro/2022101.
Abdi, Ahmad, Gérard Cornuéjols, and Giacomo Zambelli. "Arc Connectivity and Submodular Flows in Digraphs." Combinatorica, May 28, 2024. http://dx.doi.org/10.1007/s00493-024-00108-0.
Dissertations / Theses on the topic "Box-Totally dual integral polyhedron":
Pisanu, Francesco. "On box-total dual integrality and total equimodularity." Electronic Thesis or Diss., Paris 13, 2023. http://www.theses.fr/2023PA131044.
In this thesis, we study box-totally dual integral (box-TDI) polyhedra associated with severalproblems and totally equimodular matrices. Moreover, we study the complexity of some funda-mental questions related to them.We start by considering totally equimodular matrices, which are matrices such that, forevery subset of linearly independent rows, all nonsingular maximal submatrices have the samedeterminant in absolute value. Despite their similarities with totally unimodular matrices, wehighlight several differences, even in the case of incidence and adjacency matrices of graphs.As is well-known, the incidence matrix of a given graph is totally unimodular if and only if thegraph is bipartite. However, the total equimodularity of an incidence matrix depends on whetherwe consider the vertex-edge or the edge-vertex representation. We provide characterizations forboth cases. As a consequence, we prove that recognizing whether a given polyhedron is box-TDIis a co-NP-complete problem.Characterizing the total unimodularity or total equimodularity of the adjacency matrix of agiven bipartite graph remains unsolved, while we solved the corresponding problem in the case oftotal equimodularity when the graph is nonbipartite.In a later part of this work, we characterize the graphs for which the perfect matching polytope(PMP) is described by trivial inequalities and the inequalities corresponding to tight cuts. Tightcuts are defined as cuts that share precisely one edge with each perfect matching. We thenprove that any graph for which the corresponding PMP is box-TDI belongs to this class. Asa consequence, it turns out that recognizing whether the PMP is box-TDI is a polynomial-timeproblem. However, we provide several counterexamples showing that this class of graphs does notguarantee the box-TDIness of the PMP.Lastly, we present necessary conditions for the box-TDIness of the edge cover polytope andcharacterize the box-TDIness of the extendable matching polytope, which is the convex hull ofthe matchings included in a perfect matching