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546
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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vertex cover, maximum satisfiability, maximum cut, metric TSP, Steiner trees and shortest superstring. We also improve upon the clique hardness results of Feige, Goldwasser, Lovász, Safra and Szegedy [42], and Arora and Safra [6] and shows that there exists a positive ɛ such that approximating
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
The EdgeWeighted Clique problem: valid inequalities, facets and polyhedral computations
, 1997
"... Let Kn = (V; E) be the complete undirected graph with weights c e associated to the edges in E. We consider the problem of finding the subclique C = (U; F ) of Kn such that the sum of the weights of the edges in F is maximized and jU j b, for some b 2 [1; : : : ; n]. This problem is called the Maxi ..."
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Cited by 6 (1 self)
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the Maximum EdgeWeighted Clique Problem (MEWCP) and is NPhard. In this paper we investigate the facial structure of the polytope associated to the MEWCP and introduce new classes of facets for this polytope. Computational experiments with a branchandcut algorithm are reported confirming the strength
Dynamic Programming and Clique Based Approaches for Protein Threading with Profiles and Constraints ∗
, 2006
"... SUMMARY The protein threading problem with profiles is known to be efficiently solvable using dynamic programming. In this paper, we consider a variant of the protein threading problem with profiles in which constraints on distances between residues are given. We prove that protein threading with pr ..."
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edgeweight clique problem, whereas BBDPTHREAD combines dynamic programming and branchandbound techniques. We perform computational experiments using protein structure data in PDB (Protein Data Bank) using simulated distance constraints. The results show that constraints are useful to improve the alignment
Large scale protein sidechain packing based on maximum edgeweight clique ¯nding algorithm
 Proc. 2005 International Joint Conference of InCoB, AASBi, and KSBI(BIOINFO2005
"... The protein sidechain packing problem is computationally known to be NPcomplete [1]. A number of approaches has been proposed for sidechain packing. As the size of the protein becomes larger, the sampling space increases exponentially. Hence, large scale protein sidechain packing In this regard, ..."
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Cited by 1 (1 self)
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, we had also presented a maximum edgeweight clique based algorithm for protein
Protein Sidechain Positioning 1 A Maximum Edgeweight Clique Finding Algorithmic Approach for Solving Protein Sidechain Positioning Problem
"... We have developed a novel approach to solve the protein sidechain packing problem using the notion of a maximum edgeweight clique. Our approach is based on efficient reduction of protein sidechain packing problem to a graph and then solving the reduced graph to find the maximum clique. Since our ..."
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We have developed a novel approach to solve the protein sidechain packing problem using the notion of a maximum edgeweight clique. Our approach is based on efficient reduction of protein sidechain packing problem to a graph and then solving the reduced graph to find the maximum clique. Since our
A Fast Algorithm for the Maximum Clique Problem
 DISCRETE APPL. MATH
"... Given a graph, in the maximum clique problem one wants to find ..."
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Cited by 102 (2 self)
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Given a graph, in the maximum clique problem one wants to find
A Lagrangian Relaxation Approach to the EdgeWeighted Clique Problem
 European Journal of Operational Research
, 1999
"... The bclique polytope CP n b is the convex hull of the node and edge incidence vectors of all subcliques of size at most b of a complete graph on n nodes. Including the Boolean quadric polytope QP n = CP n n as a special case and being closely related to the quadratic knapsack polytope, it has recei ..."
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Cited by 16 (0 self)
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The bclique polytope CP n b is the convex hull of the node and edge incidence vectors of all subcliques of size at most b of a complete graph on n nodes. Including the Boolean quadric polytope QP n = CP n n as a special case and being closely related to the quadratic knapsack polytope, it has
Reactive Local Search for the Maximum Clique Problem
 Algorithmica
"... A new Reactive Local Search (RLS ) algorithm is proposed for the solution of the MaximumClique problem. RLS is based on local search complemented by a feedback (historysensitive) scheme to determine the amount of diversification. The reaction acts on the single parameter that decides the temporary ..."
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Cited by 96 (14 self)
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A new Reactive Local Search (RLS ) algorithm is proposed for the solution of the MaximumClique problem. RLS is based on local search complemented by a feedback (historysensitive) scheme to determine the amount of diversification. The reaction acts on the single parameter that decides
Results 1  10
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546