TY  - BOOK
AU  - Arthanari,Tirukkattuppalli Subramanyam
TI  - Pedigree Polytopes: New Insights on Computational Complexity of Combinatorial Optimisation Problems 
SN  - 9789811999529
U1  - 511.352 23
PY  - 2023///
CY  - Singapore
PB  - Springer Nature Singapore, Imprint: Springer
KW  - Computational complexity
KW  - Mathematical optimization
KW  - Calculus of variations
KW  - Algebraic fields
KW  - Polynomials
KW  - Operations research
KW  - Management science
KW  - Computational Complexity
KW  - Optimization
KW  - Calculus of Variations and Optimization
KW  - Continuous Optimization
KW  - Field Theory and Polynomials
KW  - Operations Research, Management Science
N1  - Chapter 1: Prologue -- Chapter 2: Notations, Definitions and Briefs -- Chapter 3: Motivation for Studying Pedigrees -- Chapter 4: Structure of the Pedigree Polytope -- Chapter 5: Membership Checking in Pedigree Polytopes -- Chapter 6: Computational Complexity of Membership Checking -- Chapter 7: Efficient Checking of Membership in Pedigree Polytope and its Implications -- Chapter 8: Epilogue
N2  - 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 these proofs 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
UR  - https://doi.org/10.1007/978-981-19-9952-9
ER  -