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Exact algorithms fo...
Exact algorithms for exact satisfiability and number of perfect matchings
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- Björklund, Andreas (författare)
- Lund University,Lunds universitet,Institutionen för datavetenskap,Institutioner vid LTH,Lunds Tekniska Högskola,Department of Computer Science,Departments at LTH,Faculty of Engineering, LTH
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- Husfeldt, Thore (författare)
- Lund University,Lunds universitet,Data Vetenskap,Naturvetenskapliga fakulteten,Computer Science,Faculty of Science
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(creator_code:org_t)
- Berlin, Heidelberg : Springer Berlin Heidelberg, 2006
- 2006
- Engelska.
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Ingår i: Lecture Notes in Computer Science (Automata, Languages and Programming. Proceedings, Part I). - Berlin, Heidelberg : Springer Berlin Heidelberg. - 0302-9743 .- 1611-3349. - 9783540359043 ; 4051, s. 548-559
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences -- Computer Sciences (hsv//eng)
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