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SAT-Variable Complexity of Hard Combinatorial Problems

by Kazuo Iwama, Shuichi Miyazaki - IN PROCEEDINGS OF THE WORLD COMPUTER CONGRESS OF THE IFIP , 1994
"... This paper discusses polynomial-time reductions from Hamiltonian Circuit (HC), k-Vertex Coloring (k-VC), and k-Clique 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 ..."
Abstract - Cited by 20 (0 self) - Add to MetaCart
;s), and log n + (k 0 1) log D for k-Clique (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

by Henry Wolkowicz
"... 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 interior-point methods. In this ..."
Abstract - Cited by 2 (2 self) - Add to MetaCart
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 interior-point methods. In this

Solving Hard Combinatorial Problems with GSAT -- a Case Study

by Holger H. Hoos - IN KI-96, VOLUME 1137 OF LNAI, 107--119 , 1996
"... In this paper, we investigate whether hard combinatorial problems such as the Hamiltonian circuit problem HCP (an NP-complete problem from graph theory) can be practically solved by transformation to the propositional satisfiability problem (SAT) and application of fast universal SAT-algorithms li ..."
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In this paper, we investigate whether hard combinatorial problems such as the Hamiltonian circuit problem HCP (an NP-complete 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

by Martin Grötschel, Manfred Padberg , 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 ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
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 Many-Body Interactions to Solve Hard Combinatorial Problems

by Haiqing Wei, Xin Xue , 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

by Peter Cheeseman, Bob Kanefsky, William M. Taylor - IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI-91),VOLUME 1 , 1991
"... It is well known that for many NP-complete problems, such as K-Sat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NP-complete problems can be summarized by at least one "order parameter", and that the hard p ..."
Abstract - Cited by 683 (1 self) - Add to MetaCart
It is well known that for many NP-complete problems, such as K-Sat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NP-complete problems can be summarized by at least one "order parameter", and that the hard

Molecular Computation Of Solutions To Combinatorial Problems

by Leonard M. Adleman , 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 ..."
Abstract - Cited by 773 (6 self) - Add to MetaCart
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

by Sanjeev Arora, Carsten Lund, Rajeev Motwani, Madhu Sudan, Mario Szegedy - 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 ..."
Abstract - Cited by 797 (39 self) - Add to MetaCart
in the proof (though this number is a very slowly growing function of the input length). As a consequence we prove that no MAX SNP-hard 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

by Bart Selman, Hector Levesque, David Mitchell - 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 ..."
Abstract - Cited by 730 (21 self) - Add to MetaCart
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

by Farid Alizadeh - 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 ..."
Abstract - Cited by 547 (12 self) - Add to MetaCart
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 0-1 integer programs, the maximum clique
Results 1 - 10 of 37,215