Biclique Partitions, Biclique Covers, and Disjunctive Constraints

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dc.contributor.advisorHicks, Illya V.
dc.creatorLyu, Bochuan
dc.date.accessioned2023-08-09T16:36:38Z
dc.date.available2023-08-09T16:36:38Z
dc.date.created2023-05
dc.date.issued2023-04-20
dc.date.submittedMay 2023
dc.date.updated2023-08-09T16:36:38Z
dc.description.abstractThis thesis focuses on disjunctive constraints and related combinatorial optimization problems: minimum biclique partition problem and minimum biclique cover problem. We introduce techniques to build small ideal mixed-integer programming (MIP) formulations of combinatorial disjunctive constraints (CDCs) via the independent branching scheme. We present a pairwise IB-representable class of CDCs, CDCs admitting junction trees, and provide a combinatorial procedure to build MIP formulations for those constraints. An NP-complete combinatorial optimization problem, the minimum biclique cover problem, needs to be solved in the combinatorial procedure. It motivates us to study minimum biclique partition and biclique cover problems on co-chordal graphs, which is the complementary graph of chordal. We provide heuristics to find biclique partitions on co-chordal graphs and show that the heuristics can provide biclique partitions close to optimal or even optimal if the graphs satisfy further assumptions on the structures. In addition, we provide a tighter bound for minimum biclique covers on a subclass of co-chordal graphs and present a lower bound for minimum biclique covers of general graphs. We also investigate the disjunctive constraints for piecewise linear relaxations of univariate and high-dimensional nonlinear functions that could appear in optimization problems. In order to study those piecewise linear relaxations, we introduce a new class of combinatorial disjunctive constraints: generalized n-dimensional ordered CDCs and present logarithmically sized ideal formulations under the independent branching scheme.
dc.format.mimetypeapplication/pdf
dc.identifier.citationLyu, Bochuan. "Biclique Partitions, Biclique Covers, and Disjunctive Constraints." (2023) Diss., Rice University. <a href="https://hdl.handle.net/1911/115102">https://hdl.handle.net/1911/115102</a>.
dc.identifier.urihttps://hdl.handle.net/1911/115102
dc.language.isoeng
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
dc.subjectBiclique Partitions
dc.subjectBiclique Covers
dc.subjectDisjunctive Constraints
dc.titleBiclique Partitions, Biclique Covers, and Disjunctive Constraints
dc.typeThesis
dc.type.materialText
thesis.degree.departmentComputational and Applied Mathematics
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
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