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by Hantao Zhang, Haiou Shen, Felip Manyà
http://www.cs.uiowa.edu/~hshen/maxsat.pdf
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Abstract:
The maximum satisfiability problem (MAX-SAT) is stated as follows: Given a boolean formula in CNF, find a truth assignment that satisfies the maximum possible number of its clauses. MAX-SAT is MAX-SNP-complete and received much attention recently. One of the challenges posed by Alber, Gramm and Niedermeier in a recent survey paper asks: Can MAX-SAT be solved in less than 2 n “steps”? Here, n is the number of distinct variables in the formula and a step may take polynomial time of the input. We answered this challenge positively by showing that a popular algorithm based on branch-and-bound is bounded by O(b2 n) in time, where b is the maximum number of occurrences of any variable in the input. When the input formula is in 2-CNF, that is, each clause has at most two literals, MAX-SAT becomes MAX-2-SAT and the decision version of MAX-2-SAT is still NP-complete. The best bound of the known algorithms for MAX-2-SAT is O(m2 m/5), where m is the number of clauses. We propose an efficient decision algorithm for MAX-2-SAT whose time complexity is bound by O(n2 n). This result is substantially better than the previously known results. Experimental results also show that our algorithm outperforms any algorithm we know on MAX-2-SAT.
Citations
|
778
|
A computing procedure for quantification theory
– Davis, Putnam
- 1960
|
|
307
|
A machine program for theorem-proving
– Davis, Logemann, et al.
- 1962
|
|
130
|
Improvements to propositional satisfiability search algorithms
– Freeman
- 1995
|
|
97
|
Solving propositional satisfiability problems
– Jeroslow, Wang
- 1990
|
|
86
|
Algorithms for the maximum satisfiability problem
– Hansen, Jaumard
- 1990
|
|
79
|
Hardness of approximations
– Arora, Lund
- 1995
|
|
51
|
A deterministic (2 − 2/(k + 1)) n algorithm for k–SAT based on local search. Theoretical Computer Science
– Dantsin, Goerdt, et al.
- 2002
|
|
49
|
A two-phase exact algorithm for MAX-SAT and weighted MAXSAT problems
– Borchers, Furman
- 1999
|
|
44
|
Parameterizing above guaranteed values: MaxSat and MaxCut
– Mahajan, Raman
- 1999
|
|
38
|
Upper bounds for MaxSat: Further improved
– Bansal, Raman
- 1999
|
|
34
|
Generic ILP versus specialized 0-1 ILP: an update
– Aloul, Ramani, et al.
- 2002
|
|
34
|
New worst-case upper bounds for SAT
– Hirsch
- 2000
|
|
33
|
Pure Literal Look Ahead: An O(1:497) 3-Satisfiability Algorithm
– Schiermeyer
- 1996
|
|
26
|
Faster exact algorithms for hard problems: a parameterized point of view
– Alber, Gramm, et al.
- 2001
|
|
25
|
New upper bounds for maximum satisfiability
– Niedermeier, Rossmanith
- 2000
|
|
18
|
Rossmanith: New worst-case upper bounds for MAX-2-SAT with application to MAX-CUT
– Gramm, Hirsch, et al.
|
|
16
|
Comparative studies of constraint satisfaction and davis-putnam algorithms for maximum satis ability problems
– Wallace, Freuder
- 1996
|
|
15
|
A linear programming and rounding approach to Max 2-Sat
– Cheriyan, Cunningnham, et al.
- 1996
|
|
14
|
Improved branch and bound algorithms for Max-SAT
– Alsinet, Manyà, et al.
|
|
11
|
A new algorithm for MAX-2-SAT
– Hirsch
- 2000
|
|
5
|
Some prospects for efficient fixed parameter algorithms
– Niedermeier
- 1998
|
|
5
|
An empirical study of max-2-sat phase transitions
– Shen, Zhang
- 2003
|
|
3
|
sub-SAT: A formulation for related boolean satisfiability with applications in routing. ISPD’02
– Xu, Rutenbar, et al.
- 2002
|
