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On Problems as Hard as CNFSat
, 2012
"... Exact exponential time algorithms for NPhard problems have thrived over the last decade. Nontrivial exponential time algorithms have been found for a myriad of problems, including Graph Coloring, Hamiltonian Path, Dominating Set and 3–CNFSat, that is, satisfiability of 3CNF formulas. For some ba ..."
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Cited by 15 (4 self)
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Exact exponential time algorithms for NPhard problems have thrived over the last decade. Nontrivial exponential time algorithms have been found for a myriad of problems, including Graph Coloring, Hamiltonian Path, Dominating Set and 3–CNFSat, that is, satisfiability of 3CNF formulas. For some
Guiding CNFSAT Search via Efficient Constraint Partitioning
 SUBMITTED TO ICCAD’04
, 2004
"... Contemporary techniques to identify a good variable order for SAT rely on identifying minimum treewidth decompositions. However, the problem finding a minimal width tree decomposition for an arbitrary graph is NP complete. The available tools and methods are impratical, as they cannot handle larg ..."
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Cited by 5 (1 self)
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large and hardtosolve CNFSAT instances. This paper proposes a novel hypergraph partitioning based constraint decomposition technique as an alternative to contemporary methods. We model the CNFSAT problem on a hypergraph and apply mincut based bipartitioning. Clausevariable statistics across
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
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
Scheduling Algorithms for Multiprogramming in a HardRealTime Environment
, 1973
"... The problem of multiprogram scheduling on a single processor is studied from the viewpoint... ..."
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Cited by 3756 (3 self)
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The problem of multiprogram scheduling on a single processor is studied from the viewpoint...
Pushing the Envelope: Planning, Propositional Logic, and Stochastic Search
, 1996
"... Planning is a notoriously hard combinatorial search problem. In many interesting domains, current planning algorithms fail to scale up gracefully. By combining a general, stochastic search algorithm and appropriate problem encodings based on propositional logic, we are able to solve hard planning pr ..."
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Cited by 579 (33 self)
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Planning is a notoriously hard combinatorial search problem. In many interesting domains, current planning algorithms fail to scale up gracefully. By combining a general, stochastic search algorithm and appropriate problem encodings based on propositional logic, we are able to solve hard planning
PolynomialTime Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
 SIAM J. on Computing
, 1997
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 1277 (4 self)
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. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and which have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 776 (5 self)
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Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhard
Good features to track
, 1994
"... No featurebased vision system can work unless good features can be identified and tracked from frame to frame. Although tracking itself is by and large a solved problem, selecting features that can be tracked well and correspond to physical points in the world is still hard. We propose a feature se ..."
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Cited by 2050 (14 self)
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No featurebased vision system can work unless good features can be identified and tracked from frame to frame. Although tracking itself is by and large a solved problem, selecting features that can be tracked well and correspond to physical points in the world is still hard. We propose a feature
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