TY - JOUR

T1 - Sub-coloring and hypo-coloring interval graphs

AU - Gandhi, Rajiv

AU - Greening, Bradford

AU - Pemmaraju, Sriram

AU - Raman, Rajiv

N1 - Funding Information: ∗Part of this work was done when the first author was visiting the University of Iowa. Research partially supported by Rutgers University Research Council Grant and by NSF award CCF-0830569. Funding Information: Part of this work was done when the first author was visiting the University of Iowa. Research partially supported by Rutgers University Research Council Grant and by NSF award CCF-0830569. Publisher Copyright: © 2010 World Scientific Publishing Company.

PY - 2010/9/1

Y1 - 2010/9/1

N2 - In this paper, we study the sub-coloring and hypo-coloring problems on interval graphs. These problems have applications in job scheduling and distributed computing and can be used as "subroutines" for other combinatorial optimization problems. In the sub-coloring problem, given a graph G, we want to partition the vertices of G into minimum number of sub-color classes, where each sub-color class induces a union of disjoint cliques in G. In the hypo-coloring problem, given a graph G, and integral weights on vertices, we want to find a partition of the vertices of G into sub-color classes such that the sum of the weights of the heaviest cliques in each sub-color class is minimized. We present a "forbidden subgraph" characterization of graphs with sub-chromatic number k and use this to derive a 3-approximation algorithm for sub-coloring interval graphs. For the hypo-coloring problem on interval graphs, we first show that it is NP-complete, and then via reduction to the max-coloring problem, show how to obtain an O(log n)-approximation algorithm for it.

AB - In this paper, we study the sub-coloring and hypo-coloring problems on interval graphs. These problems have applications in job scheduling and distributed computing and can be used as "subroutines" for other combinatorial optimization problems. In the sub-coloring problem, given a graph G, we want to partition the vertices of G into minimum number of sub-color classes, where each sub-color class induces a union of disjoint cliques in G. In the hypo-coloring problem, given a graph G, and integral weights on vertices, we want to find a partition of the vertices of G into sub-color classes such that the sum of the weights of the heaviest cliques in each sub-color class is minimized. We present a "forbidden subgraph" characterization of graphs with sub-chromatic number k and use this to derive a 3-approximation algorithm for sub-coloring interval graphs. For the hypo-coloring problem on interval graphs, we first show that it is NP-complete, and then via reduction to the max-coloring problem, show how to obtain an O(log n)-approximation algorithm for it.

KW - NP-complete

KW - Sub-coloring

KW - approximation algorithm

KW - hypo-coloring

KW - interval graphs

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U2 - https://doi.org/10.1142/S1793830910000693

DO - https://doi.org/10.1142/S1793830910000693

M3 - Article

VL - 2

SP - 331

EP - 345

JO - Discrete Mathematics, Algorithms and Applications

JF - Discrete Mathematics, Algorithms and Applications

SN - 1793-8309

IS - 3

ER -