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Solving the maximum edge weight clique problem via unconstrained quadratic programming
- DISCRETE OPTIMIZATION
, 2007
"... The unconstrained quadratic binary program (UQP) is proving to be a successful modeling and solution framework for a variety of combinatorial optimization problems. Experience reported in the literature with several problem classes has demonstrated that this approach works surprisingly well in terms ..."
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Cited by 4 (0 self)
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in terms of solution quality and computational times, often rivaling and sometimes surpassing more traditional methods. In this paper we report on the application of UQP to the maximum edge-weighted clique problem. Computational experience is reported illustrating the attractiveness of the approach.
Solving the maximum edge weight clique problem via unconstrained quadratic programming
, 2004
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Large scale protein side-chain packing based on maximum edge-weight clique ¯nding algorithm
- Proc. 2005 International Joint Conference of InCoB, AASBi, and KSBI(BIOINFO2005
"... The protein side-chain packing problem is computationally known to be NP-complete [1]. A number of approaches has been proposed for side-chain packing. As the size of the protein becomes larger, the sampling space increases exponentially. Hence, large scale protein side-chain packing In this regard, ..."
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Cited by 1 (1 self)
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, we had also presented a maximum edge-weight clique based algorithm for protein
Protein Side-chain Positioning 1 A Maximum Edge-weight Clique Finding Algorithmic Approach for Solving Protein Side-chain Positioning Problem
"... We have developed a novel approach to solve the protein side-chain packing problem using the notion of a maximum edge-weight clique. Our approach is based on efficient reduction of protein side-chain 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 side-chain packing problem using the notion of a maximum edge-weight clique. Our approach is based on efficient reduction of protein side-chain packing problem to a graph and then solving the reduced graph to find the maximum clique. Since our
Multiple Methods for Protein Side Chain Packing Using Maximum Weight Cliques
"... In this paper, we present several methods for computing a solution to the protein side chain packing problem, with all methods having a common solution approach of breaking the polymer into subpolymers and using maximum edge weight cliques to prune the search space for the optimal side chain packing ..."
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In this paper, we present several methods for computing a solution to the protein side chain packing problem, with all methods having a common solution approach of breaking the polymer into subpolymers and using maximum edge weight cliques to prune the search space for the optimal side chain
The Edge-Weighted 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 Edge-Weighted Clique Problem (MEWCP) and is NP-hard. 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 branch-and-cut algorithm are reported confirming the strength
Maximum Dispersion and Geometric Maximum Weight Cliques
, 2000
"... We consider geometric instances of the problem of finding a set of k vertices in a complete graph with nonnegative edge weights. In particular, we present algorithmic results for the case where vertices are represented by points in d-dimensional space, and edge weights correspond to rectilinear ..."
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Cited by 14 (2 self)
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We consider geometric instances of the problem of finding a set of k vertices in a complete graph with nonnegative edge weights. In particular, we present algorithmic results for the case where vertices are represented by points in d-dimensional space, and edge weights correspond to rectilinear
1 Maximum Clique Problem
"... Let G = (V, E) be a graph without direction and weight, V = {1, 2, · · · , n} a set of vertices and E = {(i, j)|i, j ∈ V, i � = j, 1 ≤ i, j ≤ n} a set of edges. Here n ≥ 1 is an integer. Denote G = (V, E) which means the complement graph of G, where E = {(i, j)|i, j ∈ V, (i, j) / ∈ E}. Denote by ..."
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Let G = (V, E) be a graph without direction and weight, V = {1, 2, · · · , n} a set of vertices and E = {(i, j)|i, j ∈ V, i � = j, 1 ≤ i, j ≤ n} a set of edges. Here n ≥ 1 is an integer. Denote G = (V, E) which means the complement graph of G, where E = {(i, j)|i, j ∈ V, (i, j) / ∈ E}. Denote
Clique based algorithms for protein threading with profiles and constraints
- Proc. 3rd Asia Pacific Bioinformatics Conference (APBC2005), pp.51–64
, 2005
"... Protein threading with profiles in which constraints on distances between residues are given is known to be NP-hard. Moreover, a simple algorithm known as CLIQUETHREAD based on efficient reduction to maximum edge-weight clique finding problem has been known to be a practical algorithm for solving th ..."
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Cited by 1 (1 self)
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Protein threading with profiles in which constraints on distances between residues are given is known to be NP-hard. Moreover, a simple algorithm known as CLIQUETHREAD based on efficient reduction to maximum edge-weight clique finding problem has been known to be a practical algorithm for solving
Extending Bron Kerbosch for the Maximum Weight Clique Problem
"... Abstract. This contribution extends the Bron Kerbosch algorithm for solving the maximum weight clique problem, where continuous-valued weights are assigned to both, vertices and edges. We applied the proposed algorithm to graph matching problems. 1 ..."
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Abstract. This contribution extends the Bron Kerbosch algorithm for solving the maximum weight clique problem, where continuous-valued weights are assigned to both, vertices and edges. We applied the proposed algorithm to graph matching problems. 1
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