Exact Exponential Algorithms

1. Front Matter

   Pages i-xiii

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2. Introduction

   • Fedor V. Fomin, Dieter Kratsch

   Pages 1-11

3. Branching

   • Fedor V. Fomin, Dieter Kratsch

   Pages 13-30

4. Dynamic Programming

   • Fedor V. Fomin, Dieter Kratsch

   Pages 31-49

5. Inclusion-Exclusion

   • Fedor V. Fomin, Dieter Kratsch

   Pages 51-75

6. Treewidth

   • Fedor V. Fomin, Dieter Kratsch

   Pages 77-100

7. Measure & Conquer

   • Fedor V. Fomin, Dieter Kratsch

   Pages 101-124

8. Subset Convolution

   • Fedor V. Fomin, Dieter Kratsch

   Pages 125-139

9. Local Search and SAT

   • Fedor V. Fomin, Dieter Kratsch

   Pages 141-151

10. Split and List

    • Fedor V. Fomin, Dieter Kratsch

    Pages 153-160

11. Time Versus Space

    • Fedor V. Fomin, Dieter Kratsch

    Pages 161-170

12. Miscellaneous

    • Fedor V. Fomin, Dieter Kratsch

    Pages 171-185

13. Conclusions, Open Problems and Further Directions

    • Fedor V. Fomin, Dieter Kratsch

    Pages 187-188

14. Back Matter

    Pages 189-203

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For a long time computer scientists have distinguished between fast and slow algo rithms. Fast (or good) algorithms are the algorithms that run in polynomial time, which means that the number of steps required for the algorithm to solve a problem is bounded by some polynomial in the length of the input. All other algorithms are slow (or bad). The running time of slow algorithms is usually exponential. This book is about bad algorithms. There are several reasons why we are interested in exponential time algorithms. Most of us believe that there are many natural problems which cannot be solved by polynomial time algorithms. The most famous and oldest family of hard problems is the family of NP complete problems. Most likely there are no polynomial time al gorithms solving these hard problems and in the worst case scenario the exponential running time is unavoidable. Every combinatorial problem is solvable in ?nite time by enumerating all possi ble solutions, i. e. by brute force search. But is brute force search always unavoid able? De?nitely not. Already in the nineteen sixties and seventies it was known that some NP complete problems can be solved signi?cantly faster than by brute force search. Three classic examples are the following algorithms for the TRAVELLING SALESMAN problem, MAXIMUM INDEPENDENT SET, and COLORING.

• Branching
• Combinatorics
• Dynamic programming
• Exact algorithms
• Exponential algorithms
• Graph
• Hard optimization
• Satisfiability
• Vertex
• algorithms
• operations research
• optimization
• algorithm analysis and problem complexity

• Inst. Informatics, University of Bergen, Bergen, Norway

  Fedor V. Fomin

• LITA, UFR MIM, Department of Informatics, Université Paul Verlaine-Metz, Metz Cedex 01, France

  Dieter Kratsch

The authors are highly regarded academics and educators in theoretical computer science, and in algorithmics in particular.

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