Exact Exponential Algorithms

  • Fedor V. Fomin
  • Dieter Kratsch

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Fedor V. Fomin, Dieter Kratsch
    Pages 1-11
  3. Fedor V. Fomin, Dieter Kratsch
    Pages 13-30
  4. Fedor V. Fomin, Dieter Kratsch
    Pages 31-49
  5. Fedor V. Fomin, Dieter Kratsch
    Pages 51-75
  6. Fedor V. Fomin, Dieter Kratsch
    Pages 77-100
  7. Fedor V. Fomin, Dieter Kratsch
    Pages 101-124
  8. Fedor V. Fomin, Dieter Kratsch
    Pages 125-139
  9. Fedor V. Fomin, Dieter Kratsch
    Pages 141-151
  10. Fedor V. Fomin, Dieter Kratsch
    Pages 153-160
  11. Fedor V. Fomin, Dieter Kratsch
    Pages 161-170
  12. Fedor V. Fomin, Dieter Kratsch
    Pages 171-185
  13. Fedor V. Fomin, Dieter Kratsch
    Pages 187-188
  14. Back Matter
    Pages 189-203

About this book

Introduction

Today most computer scientists believe that NP-hard problems cannot be solved by polynomial-time algorithms. From the polynomial-time perspective, all NP-complete problems are equivalent but their exponential-time properties vary widely. Why do some NP-hard problems appear to be easier than others? Are there algorithmic techniques for solving hard problems that are significantly faster than the exhaustive, brute-force methods? The algorithms that address these questions are known as exact exponential algorithms.

The history of exact exponential algorithms for NP-hard problems dates back to the 1960s. The two classical examples are Bellman, Held and Karp’s dynamic programming algorithm for the traveling salesman problem and Ryser’s inclusion–exclusion formula for the permanent of a matrix. The design and analysis of exact algorithms leads to a better understanding of hard problems and initiates interesting new combinatorial and algorithmic challenges. The last decade has witnessed a rapid development of the area, with many new algorithmic techniques discovered. This has transformed  exact algorithms into a very active research field. This book provides an introduction to the area and explains the most common algorithmic techniques, and the text is supported throughout with exercises and detailed notes for further reading.

The book is intended for advanced students and researchers in computer science, operations research, optimization and combinatorics.

 

Keywords

Branching Combinatorics Dynamic programming Exact algorithms Exponential algorithms Graph Hard optimization Satisfiability Vertex algorithms operations research optimization

Authors and affiliations

  • Fedor V. Fomin
    • 1
  • Dieter Kratsch
    • 2
  1. 1.Inst. InformaticsUniversity of BergenBergenNorway
  2. 2.LITA, UFR MIM, Department of InformaticsUniversité Paul Verlaine-MetzMetz Cedex 01France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-16533-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Computer Science
  • Print ISBN 978-3-642-16532-0
  • Online ISBN 978-3-642-16533-7
  • Series Print ISSN 1862-4499
  • About this book