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

This book provides a polynomial algorithm for solving the strongly polynomial time-separable (STSP) problem, which challenges the belief that NP-complete problems cannot have polynomial algorithms. It also offers a course on efficient combinatorial optimization using max-flow and linear multicommodity flow algorithms.

Format: Hardback
Length: 221 pages
Publication date: 28 March 2023
Publisher: Springer Verlag, Singapore

This book delves into the realm of combinatorial objects, specifically focusing on a concept known as the pedigree. It not only defines the pedigree but also undertakes a comprehensive study of this object, exploring its properties and characteristics. Moreover, the book develops a theory for optimizing a linear function over the convex hull of pedigrees, known as the Pedigree polytope. A significant contribution of this work is the implementation of a robustly polynomial algorithm that facilitates the verification of membership in the pedigree polytope.

This book challenges a widely accepted notion in computer science, namely that a problem classified as NP-complete cannot be solved by a polynomial algorithm. By demonstrating that the STSP (Single-source shortest path) problem possesses a polynomial algorithm, this book provides a definitive resolution to the P versus NP question.

Throughout the book, illustrative examples, figures, and readily accessible proofs are provided to substantiate the unexpected result. These examples and proofs serve to enhance the understanding and clarity of the material, making it accessible to a broader audience.

One of the notable features of this book is the introduction of novel constructions and ideas that have not been previously utilized in the literature. These innovative approaches contribute to the depth and richness of the discussion.

Furthermore, the book employs fundamental max-flow and linear multicommodity flow algorithms and concepts in its proofs, establishing efficient membership checking for the pedigree polytope. Chapters 3 to 7 can be adopted as a course material for teaching Efficient Combinatorial Optimization.

This book represents the culmination of the author's extensive research, which commenced in 1982 with a presentation on a novel formulation of the STSP at the XIth International Symposium on Mathematical Programming in Bonn.

Weight: 541g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811999512
Edition number: 1st ed. 2023