Exact algorithms for exact satisfiability and number of perfect matchings
(2006) 33rd International Colloquium, ICALP 2006 4051. p.548-559- Abstract
- 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 characterisations. We show that the Exact Satisfiability problem of size 1 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. Using the same techniques we show how to compute Chromatic Number of an n-vertex graph in time O(2.4423(n)) and polynomial space, or time O(2.3236(n)) and... (More)
- 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 characterisations. We show that the Exact Satisfiability problem of size 1 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. Using the same techniques we show how to compute Chromatic Number of an n-vertex graph in time O(2.4423(n)) and polynomial space, or time O(2.3236(n)) and exponential space. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/395335
- author
- Björklund, Andreas LU and Husfeldt, Thore LU
- organization
- publishing date
- 2006
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Lecture Notes in Computer Science (Automata, Languages and Programming. Proceedings, Part I)
- volume
- 4051
- pages
- 548 - 559
- publisher
- Springer
- conference name
- 33rd International Colloquium, ICALP 2006
- conference location
- Venice, Italy
- conference dates
- 2006-07-10 - 2006-07-14
- external identifiers
-
- wos:000239474500048
- scopus:33746360269
- ISSN
- 0302-9743
- 1611-3349
- ISBN
- 978-3-540-35904-3
- DOI
- 10.1007/11786986
- language
- English
- LU publication?
- yes
- id
- 8f900559-36dd-4f20-b121-7ad75fa517f1 (old id 395335)
- date added to LUP
- 2016-04-01 12:37:51
- date last changed
- 2025-01-03 00:50:16
@inproceedings{8f900559-36dd-4f20-b121-7ad75fa517f1,
abstract = {{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 characterisations. We show that the Exact Satisfiability problem of size 1 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. Using the same techniques we show how to compute Chromatic Number of an n-vertex graph in time O(2.4423(n)) and polynomial space, or time O(2.3236(n)) and exponential space.}},
author = {{Björklund, Andreas and Husfeldt, Thore}},
booktitle = {{Lecture Notes in Computer Science (Automata, Languages and Programming. Proceedings, Part I)}},
isbn = {{978-3-540-35904-3}},
issn = {{0302-9743}},
language = {{eng}},
pages = {{548--559}},
publisher = {{Springer}},
title = {{Exact algorithms for exact satisfiability and number of perfect matchings}},
url = {{http://dx.doi.org/10.1007/11786986}},
doi = {{10.1007/11786986}},
volume = {{4051}},
year = {{2006}},
}