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SATVariable Complexity of Hard Combinatorial Problems
 IN PROCEEDINGS OF THE WORLD COMPUTER CONGRESS OF THE IFIP
, 1994
"... This paper discusses polynomialtime reductions from Hamiltonian Circuit (HC), kVertex Coloring (kVC), and kClique Problems to Satisfiability Problem (SAT) which are efficient in the number of Boolean variables needed in SAT. We first present a basic type of reductions that need (n 0 1) log(n 0 ..."
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Cited by 20 (0 self)
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;s), and log n + (k 0 1) log D for kClique (D is the kth largest degree of the graph). Recent revolutionary progress in SAT algorithms will make it increasingly reasonable to solve (hard) combinatorial problems after reducing them to SAT. Efficiency in the above sense apparently plays a key role
SEMIDEFINITE AND LAGRANGIAN RELAXATIONS FOR HARD COMBINATORIAL PROBLEMS
"... Semidefinite Programming is currently a very exciting and active area of research. Semidefinite relaxations generally provide very tight bounds for many classes of numerically hard problems. In addition, these relaxations can be solved efficiently by interiorpoint methods. In this ..."
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Cited by 2 (2 self)
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Semidefinite Programming is currently a very exciting and active area of research. Semidefinite relaxations generally provide very tight bounds for many classes of numerically hard problems. In addition, these relaxations can be solved efficiently by interiorpoint methods. In this
Solving Hard Combinatorial Problems with GSAT  a Case Study
 IN KI96, VOLUME 1137 OF LNAI, 107119
, 1996
"... In this paper, we investigate whether hard combinatorial problems such as the Hamiltonian circuit problem HCP (an NPcomplete problem from graph theory) can be practically solved by transformation to the propositional satisfiability problem (SAT) and application of fast universal SATalgorithms li ..."
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Cited by 8 (3 self)
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In this paper, we investigate whether hard combinatorial problems such as the Hamiltonian circuit problem HCP (an NPcomplete problem from graph theory) can be practically solved by transformation to the propositional satisfiability problem (SAT) and application of fast universal SAT
Ulysses 2000: In Search of Optimal Solutions to Hard Combinatorial Problems
, 1993
"... Combinatorial optimization problems pervade many areas of human problem solving especially in the fields of business, economics and engineering. Intensive mathematical research and vast increases in raw computing power have advanced the state of the art in exact and heuristic problem solving at a pa ..."
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Cited by 2 (0 self)
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Combinatorial optimization problems pervade many areas of human problem solving especially in the fields of business, economics and engineering. Intensive mathematical research and vast increases in raw computing power have advanced the state of the art in exact and heuristic problem solving at a
Tailoring ManyBody Interactions to Solve Hard Combinatorial Problems
, 1997
"... A quantum machine consisting of interacting linear clusters of atoms is proposed for the 3SAT problem. Each cluster with two relevant states of collective motion can be used to register a Boolean variable. Given any 3SAT Boolean formula the interactions among the clusters can be so tailored that the ..."
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computers solve many problems amazingly fast. Yet there are problems hard to them in the sense that the best algorithms essentially take exponential running time. Many of the hard problems are NP even NPcomplete [1]. A problem is NP provided that it can have its answer checked in polynomial time
Where the REALLY Hard Problems Are
 IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI91),VOLUME 1
, 1991
"... It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard p ..."
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Cited by 683 (1 self)
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It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard
Molecular Computation Of Solutions To Combinatorial Problems
, 1994
"... The tools of molecular biology are used to solve an instance of the directed Hamiltonian path problem. A small graph is encoded in molecules of DNA and the `operations' of the computation are performed with standard protocols and enzymes. This experiment demonstrates the feasibility of carrying ..."
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Cited by 773 (6 self)
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The tools of molecular biology are used to solve an instance of the directed Hamiltonian path problem. A small graph is encoded in molecules of DNA and the `operations' of the computation are performed with standard protocols and enzymes. This experiment demonstrates the feasibility
Proof verification and hardness of approximation problems
 IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
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Cited by 797 (39 self)
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in the proof (though this number is a very slowly growing function of the input length). As a consequence we prove that no MAX SNPhard problem has a polynomial time approximation scheme, unless NP=P. The class MAX SNP was defined by Papadimitriou and Yannakakis [82] and hard problems for this class include
A New Method for Solving Hard Satisfiability Problems
 AAAI
, 1992
"... We introduce a greedy local search procedure called GSAT for solving propositional satisfiability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approac ..."
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Cited by 730 (21 self)
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We introduce a greedy local search procedure called GSAT for solving propositional satisfiability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 547 (12 self)
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mechanical way to algorithms for SDP with proofs of convergence and polynomial time complexity also carrying over in a similar fashion. Finally we study the significance of these results in a variety of combinatorial optimization problems including the general 01 integer programs, the maximum clique
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