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An Incremental Search Heuristic for Coloring Vertices of a Graph

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Graphs and Combinatorial Optimization: from Theory to Applications

Part of the book series: AIRO Springer Series ((AIROSS,volume 5))

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Abstract

Graph coloring is one of the fundamentally known NP-complete problem. Several heuristics have been developed to solve this problem, among which greedy coloring is the most naturally used one. In greedy coloring, vertices are traversed following an order and hence performance of it highly depends on finding a good order. In this paper, we propose an incremental search heuristic (ISH) which considers some ρ 1 random orders and for each of them it calls a selective search (SS) procedure with parameter ρ 2. Given an order, SS considers only those orders which produces equal or less number of distinct colors than a given order. We showed that those orders can be partitioned into disjoint subsets of equivalent orders. To make effective search, SS selects and evaluates only one order from such a subset. Analytically we have shown that ISH can solve the graph coloring instances on sparse graph in expected polynomial time. Through simulations, we have evaluated ISH on 86 challenging benchmarks and compare results with state of the art existing algorithms. We observed that ISH significantly outperforms existing algorithms specially for sparse graphs and also produces reasonably good results for others.

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Authors and Affiliations

  1. Advance Computing and Microelectronics Unit, Indian Statistical Institute, Kolkata, India

    Subhankar Ghosal & Sasthi C. Ghosh

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  1. Subhankar Ghosal
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  2. Sasthi C. Ghosh
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Editors and Affiliations

  1. Consiglio Nazionale delle Ricerce, Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti”, Roma, Italy

    Claudio Gentile

  2. Consiglio Nazionale delle Ricerce, Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti”, Roma, Italy

    Giuseppe Stecca

  3. Consiglio Nazionale delle Ricerce, Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti”, Roma, Italy

    Paolo Ventura

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Ghosal, S., Ghosh, S.C. (2021). An Incremental Search Heuristic for Coloring Vertices of a Graph. In: Gentile, C., Stecca, G., Ventura, P. (eds) Graphs and Combinatorial Optimization: from Theory to Applications. AIRO Springer Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-030-63072-0_4

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