Pedigree Polytopes: New Insights on Computational Complexity of Combinatorial Optimisation Problems

ISBN-13: 9789811999512 / Angielski

Tirukkattuppalli Subramanyam Arthanari

Opis

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.

Spis treści

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.

O autorze

Tiru Arthanari is serving the Department of Information Systems and Operations Management, University of Auckland, Auckland, New Zealand, contributing to the research environment. Tiru was awarded the International Anassilaos Award, Renato Calapso Prize for mathematics, at Reggio Calabria, Italy, in 2014. He received the ‘Lifetime Achievement Award’ from the Operations Research Society of India (ORSI) for outstanding contributions towards the promotion of operations research in India. Tiru was Head of the Indian Statistical Institute, Bangalore Centre, before moving to New Zealand. He has international recognition for his research showing most statistical problems are essentially constrained optimization problems, from his Wiley classic book, ‘Mathematical programming in statistics’ (with Y Dodge).

Tiru is Fellow and Life Member of the Indian Society for Probability and Statistics and Fellow and Life Member of the Operations Research Society of India. Tiru Arthanari is Adjunct Professor at C.R. Rao Advanced Institute of Mathematics, Statistics and Computer Science (AIMSCS, Hyderabad, India). He was elected as a corresponding member to the Accademia Peloritana Dei Pericolanti, established in 1729 in Sicily. He received the best paper award in 2016 for his paper published in JAIS. Tiru received the Research Excellence Award 2017 from the Business school. Tiru has published research articles in Discrete Mathematics, Discrete Applied Mathematics, Annals of Operations Research, European Journal of Operations Research, Discrete Optimization, Journal of the Association for Information Systems, International Journal of Production Economics, Journal of Cleaner Production, Journal of Operations & Production Management, Applied Economics, and Quality Engineering, among others.