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New methods for 3SAT decision and worstcase analysis
 THEORETICAL COMPUTER SCIENCE
, 1999
"... We prove the worstcase upper bound 1:5045 n for the time complexity of 3SAT decision, where n is the number of variables in the input formula, introducing new methods for the analysis as well as new algorithmic techniques. We add new 2 and 3clauses, called "blocked clauses", generalizing the e ..."
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Cited by 66 (12 self)
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We prove the worstcase upper bound 1:5045 n for the time complexity of 3SAT decision, where n is the number of variables in the input formula, introducing new methods for the analysis as well as new algorithmic techniques. We add new 2 and 3clauses, called "blocked clauses", generalizing the extension rule of "Extended Resolution." Our methods for estimating the size of trees lead to a refined measure of formula complexity of 3clausesets and can be applied also to arbitrary trees. Keywords: 3SAT, worstcase upper bounds, analysis of algorithms, Extended Resolution, blocked clauses, generalized autarkness. 1 Introduction In this paper we study the exponential part of time complexity for 3SAT decision and prove the worstcase upper bound 1:5044:: n for n the number of variables in the input formula, using new algorithmic methods as well as new methods for the analysis. These methods also deepen the already existing approaches in a systematically manner. The following results...
Improved Algorithms for 3Coloring, 3EdgeColoring, and Constraint Satisfaction
, 2001
"... We consider worst case time bounds for NPcomplete problems including 3SAT, 3coloring, 3edgecoloring, and 3list coloring. Our algorithms are based on a constraint satisfaction (CSP) formulation of these problems; 3SAT is equivalent to (2, 3)CSP while the other problems above are special cases ..."
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Cited by 47 (2 self)
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We consider worst case time bounds for NPcomplete problems including 3SAT, 3coloring, 3edgecoloring, and 3list coloring. Our algorithms are based on a constraint satisfaction (CSP) formulation of these problems; 3SAT is equivalent to (2, 3)CSP while the other problems above are special cases of (3, 2)CSP. We give a fast algorithm for (3, 2) CSP and use it to improve the time bounds for solving the other problems listed above. Our techniques involve a mixture of DavisPutnamstyle backtracking with more sophisticated matching and network flow based ideas. 1 Introduction There has recently been growing interest in analysis of superpolynomialtime algorithms, including algorithms for NPhard problems such as satisfiability or graph coloring. This interest has multiple causes: . Many important applications can be modeled with these problems, and with the increased speed of modern computers, solved effectively; for instance it is now routine to solve hard 500variable satisfia...
Deciding propositional tautologies: Algorithms and their complexity
, 1997
"... We investigate polynomial reductions and efficient branching rules for algorithms deciding propositional tautologies for DNF and coNPcomplete subclasses. Upper bounds on the time complexity are given with exponential part 2 ff\Delta(F ) where (F ) is one of the measures n(F ) = #f variables g, ` ..."
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Cited by 38 (8 self)
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We investigate polynomial reductions and efficient branching rules for algorithms deciding propositional tautologies for DNF and coNPcomplete subclasses. Upper bounds on the time complexity are given with exponential part 2 ff\Delta(F ) where (F ) is one of the measures n(F ) = #f variables g, `(F ) = #f literal occurrences g and k(F ) = #f clauses g. We start with a discussion of variants of the algorithms from [Monien/Speckenmeyer85] and [Luckhardt84] with the known upper bound 2 0:695\Deltan for 3DNF and (roughly) (2 \Delta (1 \Gamma 2 \Gammap )) n for pDNF, p 3, where p is the maximal clause length, giving now an uniform treatment for all pDNF including the easy decidable case p 2. Recently for 3DNF the bound has been lowered to 2 0:5892\Deltan ([K2]; see also [Sch2], [K3]). In this article further improvements are achieved by studying two additional characteristic groups of parameters. The first group differentiates according to the maximal numbers (a; b) of occ...
Algorithms for SAT/TAUT decision based on various measures
 Information and Computation
, 1999
"... We investigate algorithms deciding propositional tautologies for DNF and coNPcomplete subclasses given by restrictions on the number of occurrences of literals. Especially polynomial use of resolution for reductions in combination with a new combinatorial principle called "Generalized Sign Princip ..."
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Cited by 11 (8 self)
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We investigate algorithms deciding propositional tautologies for DNF and coNPcomplete subclasses given by restrictions on the number of occurrences of literals. Especially polynomial use of resolution for reductions in combination with a new combinatorial principle called "Generalized Sign Principle" is studied. Upper bounds on time complexity are given with exponential part 2 ff\Delta(F ) where the measure (F ) for a clause set F either is the number n(F ) of variables, the number `(F ) of literal occurrences or the number k(F ) of clauses. ff is called a "power coefficient" for the class of formulas under consideration w.r.t. measure . Power coefficients are derived with the help of a method estimating the size of trees, which is also used to find "good" branching rules. Under natural conditions power coefficients ff; fi; fl for n; k; ` respectively fulfill ff fi fl. We obtain the following power coefficients.  0:1112 for DNF w.r.t. `  0:3334 for DNF w.r.t. k These result...
SAT Local Search Algorithms: WorstCase Study
 Journal of Automated Reasoning
, 2000
"... Recent experiments demonstrated that local search algorithms (e.g. GSAT) are able to nd satisfying assignments for many \hard" Boolean formulas. A wide experimental study of these algorithms demonstrated their good performance on some important classes of formulas as well as poor performance on some ..."
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Cited by 11 (6 self)
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Recent experiments demonstrated that local search algorithms (e.g. GSAT) are able to nd satisfying assignments for many \hard" Boolean formulas. A wide experimental study of these algorithms demonstrated their good performance on some important classes of formulas as well as poor performance on some other ones. In contrast, theoretical knowledge of their worstcase behaviour is very limited. However, many worstcase upper and lower bounds of the form 2 n ( < 1 is a constant) are known for other SAT algorithms, e.g. resolutionlike algorithms. In the present paper we prove both upper and lower bounds of this form for local search algorithms. The class of linearsize formulas we consider for the upper bound covers most of the DIMACS benchmarks, the satisability problem for this class of formulas is NPcomplete. 1 Introduction Recently there has been an increased interest to local search algorithms for the Boolean satisability problem. Though this problem is NPcomplete (see e.g. ...
3Coloring in time O(1.3446^n): a noMIS algorithm
, 1995
"... We consider worst case time bounds for NPcomplete problems including 3SAT, 3coloring, 3edgecoloring, and 3listcoloring. Our algorithms are based on a common generalization of these problems, called symbolsystem satisfiability or, briefly, SSS [1]. 3SAT is equivalent to (2,3)SSS while the ..."
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Cited by 9 (0 self)
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We consider worst case time bounds for NPcomplete problems including 3SAT, 3coloring, 3edgecoloring, and 3listcoloring. Our algorithms are based on a common generalization of these problems, called symbolsystem satisfiability or, briefly, SSS [1]. 3SAT is equivalent to (2,3)SSS while the other problems above are special cases of (3,2)SSS; there is also a natural duality transformation from (a; b)SSS to (b; a)SSS. We give a fast algorithm for (3,2)SSS and use it to improve the time bounds for solving the other problems listed above. 1 Introduction There are many known NPcomplete problems including such important graph theoretic problems as coloring and independent sets. Unless P=NP, we know that no polynomial time algorithm for these problems can exist, but that does not obviate the need to solve them as efficiently as possible, indeed the fact that these problems are hard makes efficient algorithms for them especially important. We are interested in this paper in...
3Coloring in Time
, 2000
"... We consider worst case time bounds for NPcomplete problems including 3SAT, 3coloring, 3edgecoloring, and 3listcoloring. Our algorithms are based on a constraint satisfaction (CSP) formulation of these problems. 3SAT is equivalent to (2, 3)CSP while the other problems above are special cases ..."
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Cited by 2 (0 self)
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We consider worst case time bounds for NPcomplete problems including 3SAT, 3coloring, 3edgecoloring, and 3listcoloring. Our algorithms are based on a constraint satisfaction (CSP) formulation of these problems. 3SAT is equivalent to (2, 3)CSP while the other problems above are special cases of (3, 2)CSP; there is also a natural duality transformation from (a, b)CSP to (b, a)CSP. We give a fast algorithm for (3, 2)CSP and use it to improve the time bounds for solving the other problems listed above. Our techniques involve a mixture of DavisPutnamstyle backtracking with more sophisticated matching and network flow based ideas. 1
Improved Algorithms for 3Coloring, 3EdgeColoring, and Constraint Satisfaction
, 2000
"... We consider worst case time bounds for NPcomplete problems including 3SAT, 3coloring, 3edgecoloring, and 3listcoloring. Our algorithms are based on a constraint satisfaction (CSP) formulation of these problems; 3SAT is equivalent to (2, 3)CSP while the other problems above are special cases ..."
Abstract
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We consider worst case time bounds for NPcomplete problems including 3SAT, 3coloring, 3edgecoloring, and 3listcoloring. Our algorithms are based on a constraint satisfaction (CSP) formulation of these problems; 3SAT is equivalent to (2, 3)CSP while the other problems above are special cases of (3, 2)CSP. We give a fast algorithm for (3, 2)CSP and use it to improve the time bounds for solving the other problems listed above. Our techniques involve a mixture of DavisPutnamstyle backtracking with more sophisticated matching and network flow based ideas. 1