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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 103 (2 self)
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Given a graph, in the maximum clique problem one wants to find
Cliquedetection Models in Computational Biochemistry and Genomics
 European Journal of Operational Research
, 2005
"... Many important problems arising in computational biochemistry and genomics have been formulated in terms of underlying combinatorial optimization models. In particular, a number have been formulated as cliquedetection models. The proposed article includes an introduction to the underlying biochemis ..."
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Cited by 31 (3 self)
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Many important problems arising in computational biochemistry and genomics have been formulated in terms of underlying combinatorial optimization models. In particular, a number have been formulated as cliquedetection models. The proposed article includes an introduction to the underlying biochemistry and genomic aspects of the problems as well as to the graphtheoretic aspects of the solution approaches. Each subsequent section describes a particular type of problem, gives an example to show how the graph model can be derived, summarizes recent progress, and discusses challenges associated with solving the associated graphtheoretic models. Clique detection models include prescribing (a) a maximal clique, (b) a maximum clique, (c) a maximum weighted clique, or (d) all maximal cliques in a graph. The particular types of biochemistry and genomics problems that can be represented by a clique detection model include integration of genome mapping data, nonoverlapping local alignments, matching and comparing molecular structures, and protein docking.
An Algorithm for Finding a Maximum Clique in a Graph
, 1997
"... This paper introduces a branchandbound algorithm for the maximum clique problem which applies existing clique finding and vertex coloring heuristics to determine lower and upper bounds for the size of a maximum clique. Computational results on a variety of graphs indicate the proposed procedure in ..."
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Cited by 28 (0 self)
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This paper introduces a branchandbound algorithm for the maximum clique problem which applies existing clique finding and vertex coloring heuristics to determine lower and upper bounds for the size of a maximum clique. Computational results on a variety of graphs indicate the proposed procedure in most instances outperforms leading algorithms.
A MultiDepot Pickup and Delivery Problem with a Single Hub and Heterogeneous Vehicles
 European Journal of Operational Research
, 2000
"... This paper introduces a special kind of multidepot pickup and delivery ..."
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Cited by 12 (0 self)
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This paper introduces a special kind of multidepot pickup and delivery
An Exact Algorithm For The Maximum Stable Set Problem
 Computational Optimization and Application
, 1994
"... We describe a new branchandbound algorithm for the exact solution of the maximum cardinality stable set problem. The bounding phase is based on a variation of the standard greedy algorithm for finding a colouring of a graph. Two different nodefixing heuristics are also described. Computational te ..."
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Cited by 11 (2 self)
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We describe a new branchandbound algorithm for the exact solution of the maximum cardinality stable set problem. The bounding phase is based on a variation of the standard greedy algorithm for finding a colouring of a graph. Two different nodefixing heuristics are also described. Computational tests on random and structured graphs and very large graphs corresponding to `reallife' problems show that the algorithm is competitive with the fastest algorithms known so far. 1 Introduction We denote by G = (V; E) an undirected graph. V is the set of nodes and E the set of edges. A stable set is a subset of V such that no two nodes of the subset are pairwise adjacent. The cardinality of a maximum stable set of G will be denoted by ff(G). A clique is a subset of V with the property that all the nodes are pairwise adjacent. A clique covering is a set of disjoint cliques whose union is equal to V ; the cardinality of a minimum clique covering is denoted by `(G), and since at most one nod...
An Optimisation Algorithm for Maximum Independent Set with Applications in Map Labelling
, 1999
"... . We consider the following map labelling problem: given distinct points p1 ; p2 ; : : : ; pn in the plane, nd a set of pairwise disjoint axisparallel squares Q1 ; Q2 ; : : : ; Qn where p i is a corner of Q i . This problem reduces to that of nding a maximum independent set in a graph. We presen ..."
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Cited by 11 (1 self)
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. We consider the following map labelling problem: given distinct points p1 ; p2 ; : : : ; pn in the plane, nd a set of pairwise disjoint axisparallel squares Q1 ; Q2 ; : : : ; Qn where p i is a corner of Q i . This problem reduces to that of nding a maximum independent set in a graph. We present a branch and cut algorithm for nding maximum independent sets and apply it to independent set instances arising from map labelling. The algorithm uses a new technique for setting variables in the branch and bound tree that implicitly exploits the Euclidean nature of the independent set problems arising from map labelling. Computational experiments show that this technique contributes to controlling the size of the branch and bound tree. We also present a novel variant of the algorithm for generating violated oddhole inequalities. Using our algorithm we can nd provably optimal solutions for map labelling instances with up to 950 cities within modest computing time, a considera...
Edge Projection and the Maximum Cardinality Stable Set Problem
, 1996
"... . Edge projection is a specialization of Lov'asz and Plummer's clique projection when restricted to edges. We discuss some properties of the edge projection which are then exploited to develop a new upper bound procedure for the Maximum Cardinality Stable Set Problem (MSS Problem). The upp ..."
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Cited by 11 (1 self)
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. Edge projection is a specialization of Lov'asz and Plummer's clique projection when restricted to edges. We discuss some properties of the edge projection which are then exploited to develop a new upper bound procedure for the Maximum Cardinality Stable Set Problem (MSS Problem). The upper bound computed by our heuristic, incorporated in a branchandbound scheme in conjunction with Balas and Yu branching rule, seems to be very effective for sparse graphs, which are typically hard instances of the MSS Problem. 1. Introduction We denote by G = (V; E) an undirected graph. V is the set of nodes and E the set of edges. A stable set is a subset of V such that no two nodes of the subset are pairwise adjacent. The cardinality of a maximum stable set of G will be denoted by ff(G). When G is the empty graph, ff(G) = 0. A clique is a subset of V with the property that all the nodes are pairwise adjacent. A clique partitioning of G is a family of cliques such that each node of G is contained ...
Graph Coloring Algorithms For Fast Evaluation Of Curtis Decompositions
 Proc. DAC 99
, 1999
"... Finding the minimum column multiplicity for a bound set of variables is an important problem in Curtis decomposition. To investigate this problem, we compared two graph coloring programs: one exact, and another one based on heuristics which can give, however, provably exact results on some types of ..."
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Cited by 9 (3 self)
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Finding the minimum column multiplicity for a bound set of variables is an important problem in Curtis decomposition. To investigate this problem, we compared two graph coloring programs: one exact, and another one based on heuristics which can give, however, provably exact results on some types of graphs. These programs were incorporated into the multivalued decomposer MVGUD. We proved that the exact graph coloring is not necessary for highquality functional decomposers. Thus we improved by orders of magnitude the speed of the column multiplicity problem, with very little or no sacrifice of decomposition quality. Comparison of our experimental results with competing decomposers shows that for nearly all benchmarks our solutions are best and time is usually not too high.
A Dynamic Programming Approach for Timing and Designing Clique Algorithms
 Algorithms and Experiments (ALEX '98): Building Bridges Between Theory and Applications
, 1998
"... Traditionally, practical clique algorithms have been compared based on their performance on various random graphs. We propose a new testing methodology which permits testing to be completed in a fraction of the time required by previous methods. In addition, the range of testing can be extended to i ..."
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Cited by 7 (2 self)
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Traditionally, practical clique algorithms have been compared based on their performance on various random graphs. We propose a new testing methodology which permits testing to be completed in a fraction of the time required by previous methods. In addition, the range of testing can be extended to include problems that could not be attempted in the past because of being too time consuming. We accomplish this by applying the approach that makes dynamic programming a very effective algorithmic technique: we use tabulated estimates for the time required to solve subproblems rather than timing each exactly. Our computational experiments validate this approach. The next step is to use this workbench to develop fast new algorithms for the maximum clique problem. A mixed algorithm is an algorithm which applies different strategies for the subproblems that arise. Using the dynamic programming approach again for timing, we mechanize the process of developing table driven algorithms which apply ...
A novel evolutionary formulation of the maximum independent set problem
 JOURNAL OF COMBINATORIAL OPTIMIZATION
, 2003
"... We introduce a novel evolutionary formulation of the problem of finding a maximum independent set of a graph. The new formulation is based on the relationship that exists between a graph’s independence number and its acyclic orientations. It views such orientations as individuals and evolves them wi ..."
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Cited by 6 (2 self)
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We introduce a novel evolutionary formulation of the problem of finding a maximum independent set of a graph. The new formulation is based on the relationship that exists between a graph’s independence number and its acyclic orientations. It views such orientations as individuals and evolves them with the aid of evolutionary operators that are very heavily based on the structure of the graph and its acyclic orientations. The resulting heuristic has been tested on some of the Second DIMACS Implementation Challenge benchmark graphs, and has been found to be competitive when compared to several of the other heuristics that have also been tested on those graphs.