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On matchings and related problems in graphs, hypergraphs, and doubly stochastic matrices

Ioannis Panagiotas 1, 2
Abstract : This thesis investigates four different and related problems that arise in the area of Combinatorial Scientific Computing (CSC). The connecting link between the four examined problems is the fundamental problem of matching, which asks for the largest set of disjoint edges in a graph or hypergraph. These problems are that of maximum cardinality matching in graphs and hypergraphs, the estimation of the number of perfect matchings in graphs, and the Birkhoff–von Neumann decomposition of doubly stochastic matrices. The study of these problems is motivated by their usefulness in several domains and applications.We examine the four problems both theoretically as well as experimentally. The focus in theory allows us to discuss, analyze, and prove properties of the examined algorithms, while the experimental side of the thesis demonstrates the possible improvements and benefits of using the proposed algorithms and solutions.
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Submitted on : Wednesday, November 18, 2020 - 11:48:22 AM
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Ioannis Panagiotas. On matchings and related problems in graphs, hypergraphs, and doubly stochastic matrices. Data Structures and Algorithms [cs.DS]. Université de Lyon, 2020. English. ⟨NNT : 2020LYSEN068⟩. ⟨tel-03011794⟩

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