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Iterated Greedy Graph Coloring and the Difficulty Landscape
, 1992
"... Many heuristic algorithms have been proposed for graph coloring. The simplest is perhaps the greedy algorithm. Many variations have been proposed for this algorithm at various levels of sophistication, but it is generally assumed that the coloring will occur in a single attempt. We note that if a ne ..."
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Cited by 32 (2 self)
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Many heuristic algorithms have been proposed for graph coloring. The simplest is perhaps the greedy algorithm. Many variations have been proposed for this algorithm at various levels of sophistication, but it is generally assumed that the coloring will occur in a single attempt. We note that if a new permutation of the vertices is chosen which respects the independent sets of a previous coloring, then applying the greedy algorithm will result in a new coloring in which the number of colors used does not increase, yet may decrease. We introduce several heuristics for generating new permutations that are fast when implemented and effective in reducing the coloring number. The resulting Iterated Greedy algorithm(IG) can obtain colorings in the range 100 to 103 on graphs in G 1000; 1 2 . More interestingly, it can optimally color kcolorable graphs with k up to 60 and n = 1000, exceeding results of anything in the literature for these graphs. We couple this algorithm with several other c...
Experiments with Parallel Graph Coloring Heuristics
 In (Johnson & Trick
, 1994
"... We report on experiments with a new hybrid graph coloring algorithm, which combines a parallel version of Morgenstern's SImpasse algorithm [20], with exhaustive search. We contribute new test data arising in five different application domains, including register allocation and class scheduling. We ..."
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Cited by 22 (0 self)
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We report on experiments with a new hybrid graph coloring algorithm, which combines a parallel version of Morgenstern's SImpasse algorithm [20], with exhaustive search. We contribute new test data arising in five different application domains, including register allocation and class scheduling. We test our algorithms both on this test data and on several types of randomly generated graphs. We compare our parallel implementation, which is done on the CM5, with two simple heuristics, the Saturation algorithm of Br'elaz [4] and the Recursive Largest First (RLF) algorithm of Leighton [18]. We also compare our results with previous work reported by Morgenstern [20] and Johnson et al. [13]. Our main results are as follows. ffl On the randomly generated graphs, the performance of Hybrid is consistently better than the sequential algorithms, both in terms of speed and number of colorings produced. However, on large random graphs, our algorithms do not come close to the best colorings found ...
APPROXIMATING MAXIMUM STABLE SET AND MINIMUM GRAPH COLORING PROBLEMS WITH THE POSITIVE SEMIDEFINITE RELAXATION
"... We compute approximate solutions to the maximum stable set problem and the minimum graph coloring problem using a positive semidefinite relaxation. The positive semidefinite programs are solved using an implementation of the dual scaling algorithm that takes advantage of the sparsity inherent in m ..."
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Cited by 9 (1 self)
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We compute approximate solutions to the maximum stable set problem and the minimum graph coloring problem using a positive semidefinite relaxation. The positive semidefinite programs are solved using an implementation of the dual scaling algorithm that takes advantage of the sparsity inherent in most graphs and the structure inherent in the problem formulation. From the solution to the relaxation, we apply a randomized algorithm to find approximate maximum stable sets and a modification of a popular heuristic to find graph colorings. We obtained high quality answers for graphs with over 1000 vertices and almost 7000 edges.
Heuristics Versus Completeness for Graph Coloring
, 2000
"... We study the complexity of the problem 3Colorability when restricted to those input graphs on which a given graph coloring heuristic is able to solve the problem. The heuristics we consider include the sequential algorithm traversing the vertices of the graph in various orderings (e.g., by decreasi ..."
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We study the complexity of the problem 3Colorability when restricted to those input graphs on which a given graph coloring heuristic is able to solve the problem. The heuristics we consider include the sequential algorithm traversing the vertices of the graph in various orderings (e.g., by decreasing degree or in the recursive smallestlast order) as well as Wood's algorithm. For each heuristic considered here, we prove that the corresponding restriction of 3Colorability remains NPcomplete. 1 Introduction Graph coloring problems are of great importance in both theory and applications and have been intensely studied during the past century. Applications of constructing a graph coloring with as few colors as possible arise, for instance, in scheduling and partitioning problems (see Garey and Johnson [GJ79]). Unfortunately, the (optimization) problem of finding the chromatic number of a given graph is very complex, and even the (decision) problem of determining whether or not a given...
Local Search Techniques for Scheduling Problems: Algorithms and Software Tools
 PHD THESIS
, 2003
"... Local Search metaheuristics are an emerging class of methods for tackling combinatorial search and optimization problems, which recently have been shown to be very effective for a large number of combinatorial problems. The Local Search techniques are based on the iterative exploration of a solutio ..."
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Local Search metaheuristics are an emerging class of methods for tackling combinatorial search and optimization problems, which recently have been shown to be very effective for a large number of combinatorial problems. The Local Search techniques are based on the iterative exploration of a solution space: at each iteration, a Local Search algorithm steps from one solution to one of its “neighbors”, i.e., solutions that are (in some sense) close to the starting one. One major drawback of this family of techniques is the lack of robustness on a wide variety of problem instances. In fact, in many cases, these methods assure finding good results in reasonable running times, whereas in other cases Local Search techniques are trapped in the socalled local minima. Several approaches to the solution of this problem recently appeared in the literature. These approaches range from the employment of statistical properties (e.g., random explorations of the solution space), to the application of learning methods or hybrid techniques. In this thesis we propose an alternative approach to cope with local minima, which is based
QoS Assurance with Colocated Wireless Access Points
, 2003
"... The proposed research aims to provide the technical framework which will enable multiple Wireless LANs to provide the assured network service while being in communication range of each other. The Access Points involved compete and cooperate while keeping the overall goal of maximum system utilizatio ..."
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The proposed research aims to provide the technical framework which will enable multiple Wireless LANs to provide the assured network service while being in communication range of each other. The Access Points involved compete and cooperate while keeping the overall goal of maximum system utilization above individual optimization. We use channel access time as the means of resource allocation, while keeping the system modular so that any other unit can also be used without changing the protocol. We provide a secondary protocol to ensure robustness of our main algorithm for Access Allocation. We also
Graph kColorability through Threshold Accepting and DavisPutnam
"... Abstract: The Graph kColorability Problem (GCP) is a well known NPhard problem consisting on finding the k minimum number of colors to paint the vertexes of a graph in such a way that two any vertexes joined by an edge has always different colors. Many years ago, Simulated Annealing (SA) was used ..."
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Abstract: The Graph kColorability Problem (GCP) is a well known NPhard problem consisting on finding the k minimum number of colors to paint the vertexes of a graph in such a way that two any vertexes joined by an edge has always different colors. Many years ago, Simulated Annealing (SA) was used for graph coloring obtaining good results; however SA is not a complete algorithm and so not always gets the optimal solution. In this paper GCP is transformed into the Satisfiability Problem and then it is solved using a hybrid algorithm that uses the Threshold Accepting algorithm (a variant of SA) and the classical one literal rule of Davis & Putnam. The new algorithm is a complete one and so gets better quality that the classical simulated annealing algorithm.
An Efficient GA with Multipoint Guided Mutation for Graph Coloring Problems
"... Proper coloring of the vertices of a graph with minimum number of colors has always been of great interest of researchers in the field of soft computing. Genetic Algorithm (GA) and its application as the solution method to the Graph Coloring problem have been appreciated and worked upon by the scien ..."
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Proper coloring of the vertices of a graph with minimum number of colors has always been of great interest of researchers in the field of soft computing. Genetic Algorithm (GA) and its application as the solution method to the Graph Coloring problem have been appreciated and worked upon by the scientists almost for the last two decades. Various genetic operators such as crossover and mutation have been used in the GA probabilistically in the previous works, which distributes the promising solutions in the search space at each generation. This paper introduces a new operator, called double point Guided Mutation operator with a special feature. An evolutionary algorithm with double point Guided Mutation for the Graph Coloring problem is proposed here, which could advance the performance level of simple GA dramatically. The algorithm has been tested upon a largescale test graphs and has shown better output than the earlier works on the same problem. This paper describes the advancement of performance of simple GA applied upon the problem of graph coloring using a operator called double point Guided Mutation in association of the general genetic operators Crossover and Mutation used probabilistically. Our work is still going on for designing better algorithms.