4,669 research outputs found
An Extraction and Expansion Approach for Graph Coloring
This paper presents an extraction and expansion approach for the graph coloring problem. The extraction phase transforms a large graph into a sequence of progressively smaller graphs by removing large independent sets from the graph. The expansion phase starts by generating an approximate coloring for the smallest graph in the sequence. Then it expands the smallest graph by progressively adding back the extracted independent sets and determine a coloring for each intermediate graph. To color each graph, a simple perturbation based tabu search algorithm is used. The proposed approach is evaluated on the DIMACS challenge benchmarks showing competitive results in comparison with the state-of-the-art methods
Minimum sum coloring for large graphs with extraction and backward expansion search
The Minimum Sum Coloring Problem (MSCP) is a relevant model tightly related to the classical vertex coloring problem (VCP). MSCP is known to be NP-hard, thus solving the problem for large graphs is particular challenging. Based on the general “reduce-and-solve” principle and inspired by the work for the VCP, we present an extraction and backward expansion search approach (EBES) to compute the upper and lower bounds for the MSCP on large graphs. The extraction phase reduces the given graph by extracting large collections of pairwise disjoint large independent sets (or color classes). The backward extension phase adds the extracted independent sets to recover the intermediate graphs while optimizing the sum coloring of each intermediate graph. We assess the proposed approach on a set of 35 large benchmark graphs with 450–4000 vertices from the DIMACS and COLOR graph coloring competitions. Computational results show that EBES is able to find improved upper bounds for 19 graphs and improved lower bounds for 12 graphs
A Family of matroid intersection algorithms for the computation of approximated symbolic network functions
In recent years, the technique of simplification during generation has turned out to be very promising for the efficient computation of approximate symbolic network functions for large transistor circuits. In this paper it is shown how symbolic network functions can be simplified during their generation with any well-known symbolic network analysis method. The underlying algorithm for the different techniques is always a matroid intersection algorithm. It is shown that the most efficient technique is the two-graph method. An implementation of the simplification during generation technique with the two-graph method illustrates its benefits for the symbolic analysis of large analog circuits
Algorithms for the minimum sum coloring problem: a review
The Minimum Sum Coloring Problem (MSCP) is a variant of the well-known vertex
coloring problem which has a number of AI related applications. Due to its
theoretical and practical relevance, MSCP attracts increasing attention. The
only existing review on the problem dates back to 2004 and mainly covers the
history of MSCP and theoretical developments on specific graphs. In recent
years, the field has witnessed significant progresses on approximation
algorithms and practical solution algorithms. The purpose of this review is to
provide a comprehensive inspection of the most recent and representative MSCP
algorithms. To be informative, we identify the general framework followed by
practical solution algorithms and the key ingredients that make them
successful. By classifying the main search strategies and putting forward the
critical elements of the reviewed methods, we wish to encourage future
development of more powerful methods and motivate new applications
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