Progress in Combinatorial Optimization
Published on 10. May 2014
386 pages
978-1-4832-6453-0 (ISBN)
Description
Progress in Combinatorial Optimization provides information pertinent to the fundamental aspects of combinatorial optimization. This book discusses how to determine whether or not a particular structure exists. Organized into 21 chapters, this book begins with an overview of a polar characterization of facets of polyhedra obtained by lifting facets of lower dimensional polyhedra. This text then discusses how to obtain bounds on the value of the objective in a graph partitioning problem in terms of spectral information about the graph. Other chapters consider the notion of a triangulation of an oriented matroid and show that oriented matroid triangulation yield triangulations of the underlying polytopes. This book discusses as well the selected results and problems on perfect ad imperfect graphs. The final chapter deals with the weighted parity problem for gammoids, which can be reduced to the weighted graphic matching problem. This book is a valuable resource for mathematicians and research workers.
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Content
ContributorsPrefaceAcknowledgmentsLifting the Facets of PolyhedraPartitioning, Spectra and Linear ProgrammingOriented Matroids and Triangulations of Convex PolytopesRecent Algorithms for Two Versions of Graph Realization and Remarks on Applications to Linear ProgrammingPolynomial Algorithm to Recognize a Meyniel GraphInteger Programming Problems for Which a Simple Rounding-Type Algorithm WorksNotes on Perfect GraphsTotal Dual Integrality of Linear Inequality SystemsNumbers of Lengths for Representations of Interval OrdersSubmodular RowsGeometric Methods in Combinatorial OptimizationA Fast Algorithm That Makes Matrices Optimally SparseStructural Theory for the Combinatorial Systems Characterized by Submodular FunctionsGreedoids-A Structural Framework for the Greedy AlgorithimPreemptive Scheduling of Uniform Machines Subject to Release DatesAn Application of Matroid Polyhedral Theory to Unit-Execution Time, Tree-Precedence Job SchedulingSome Problems on Dynamic/Periodic GraphsPolytopes and ComplexityStatics and Electric Network Theory: A Unifying Role of MatroidsTotal Dual Integrality from Directed Graphs, Crossing Families, and Sub- and Supermodular FunctionsSolving the Weighted Parity Problem for Gammoids by Reduction to Graphic Matching
