Pedigree Polytopes
New Insights on Computational Complexity of Combinatorial Optimisation Problems
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Beschreibung
This book defines and studies a combinatorial object called the pedigree and develops the theory for optimising a linear function over the convex hull of pedigrees (the Pedigree polytope). A strongly polynomial algorithm implementing the framework given in the book for checking membership in the pedigree polytope is a major contribution.
This book challenges the popularly held belief in computer science that a problem included in the NP-complete class may not have a polynomial algorithm to solve. By showing STSP has a polynomial algorithm, this book settles the P vs NP question.
This book has illustrative examples, figures, and easily accessible proofs for showing this unexpected result. This book introduces novel constructions and ideas previously not used in the literature. Another interesting feature of this book is it uses basic max-flow and linear multicommodity flow algorithms and concepts in theseproofs establishing efficient membership checking for the pedigree polytope. Chapters 3-7 can be adopted to give a course on Efficient Combinatorial Optimization. This book is the culmination of the author's research that started in 1982 through a presentation on a new formulation of STSP at the XIth International Symposium on Mathematical Programming at Bonn.
This book defines and studies a combinatorial object called the pedigree and develops the theory for optimising a linear function over the convex hull of pedigrees (the Pedigree polytope). A strongly polynomial algorithm implementing the framework given in the book for checking membership in the pedigree polytope is a major contribution.
This book challenges the popularly held belief in computer science that a problem included in the NP-complete class may not have a polynomial algorithm to solve. By showing STSP has a polynomial algorithm, this book settles the P vs NP question.
This book has illustrative examples, figures, and easily accessible proofs for showing this unexpected result. This book introduces novel constructions and ideas previously not used in the literature. Another interesting feature of this book is it uses basic max-flow and linear multicommodity flow algorithms and concepts in theseproofs establishing efficient membership checking for the pedigree polytope. Chapters 3-7 can be adopted to give a course on Efficient Combinatorial Optimization. This book is the culmination of the author's research that started in 1982 through a presentation on a new formulation of STSP at the XIth International Symposium on Mathematical Programming at Bonn.
Settles an important question in Mathematics, namely the millennium problem – NP vs P Provides easily accessible proof for the same, with examples and figures even graduate students can grasp Opens up a pandora’s box of research and applied research possibilities
Autor*in
Tirukkattuppalli Subramanyam Arthanari
Themen in »Pedigree Polytopes«
Combinatorial Optimization Pedigree Polytopes Polynomial Time Algorithms Computational Complexity Symmetric Traveling Salesman Problem Combinatorial Optimisation NP vs P Polynomial Solvability NP-completeness Maximal flow problem Polyhedral Combinatorics Good algorithm Efficient algorithm
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“This book is intended for graduate or advanced undergraduate students of mathematics, computer science, and electrical engineering. The book will also be of interest to researchers … .” (Samir Kumar Neog, zbMATH 1559.90001, 2025)
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