Exact algorithms for exact satisfiability and number of perfect matchings
Author
Summary, in English
We present exact algorithms with exponential running times for variants of n-element set cover problems, based on divide-and-conquer and on inclusion exclusion characterizations. We show that the Exact Satisfiability problem of size l with m clauses can be solved in time 2(m)l(O(1)) and polynomial space. The same bounds hold for counting the number of solutions. As a special case, we can count the number of perfect matchings in an n-vertex graph in time 2(n)n(O(1)) and polynomial space. We also show how to count the number of perfect matchings in time O(1.732(n)) and exponential space. We give a number of examples where the running time can be further improved if the hypergraph corresponding to the set cover instance has low pathwidth. This yields exponential-time algorithms for counting k-dimensional matchings, Exact Uniform Set Cover, Clique Partition, and Minimum Dominating Set in graphs of degree at most three. We extend the analysis to a number of related problems such as TSP and Chromatic Number.
Department/s
- Department of Computer Science
- Computer Science
- Parallel Systems
Publishing year
2008
Language
English
Pages
226-249
Publication/Series
Algorithmica
Volume
52
Issue
2
Document type
Journal article
Publisher
Springer
Topic
- Computer Science
Keywords
- exact algorithms
- set partition
- exact satisfability
- number
- of perfect matchings
- set cover
Status
Published
Project
- Exact algorithms
Research group
- Algorithms
ISBN/ISSN/Other
- ISSN: 0178-4617