TY - JOUR

T1 - Sum coloring interval and κ-claw free graphs with application to scheduling dependent jobs

AU - Halldórsson, Magnús M.

AU - Kortsarz, Guy

AU - Shachnai, Hadas

PY - 2003/11

Y1 - 2003/11

N2 - We consider the sum coloring and sum multicoloring problems on several fundamental classes of graphs, including the classes of interval and κ-claw free graphs. We give an algorithm that approximates sum coloring within a factor of 1.796, for any graph in which the maximum κ-colorable subgraph problem is polynomially solvable. In particular, this improves on the previous best known ratio of 2 for interval graphs. We introduce a new measure of coloring, robust throughput, that indicates how "quickly" the graph is colored, and show that our algorithm approximates this measure within a factor of 1.4575. In addition, we study the contiguous (or non-preemptive) sum multicoloring problem on κ-claw free graphs. This models, for example, the scheduling of dependent jobs on multiple dedicated machines, where each job requires the exclusive use of a most κ machines. Assuming that κ is a fixed constant, we obtain the first constant factor approximation for the problem.

AB - We consider the sum coloring and sum multicoloring problems on several fundamental classes of graphs, including the classes of interval and κ-claw free graphs. We give an algorithm that approximates sum coloring within a factor of 1.796, for any graph in which the maximum κ-colorable subgraph problem is polynomially solvable. In particular, this improves on the previous best known ratio of 2 for interval graphs. We introduce a new measure of coloring, robust throughput, that indicates how "quickly" the graph is colored, and show that our algorithm approximates this measure within a factor of 1.4575. In addition, we study the contiguous (or non-preemptive) sum multicoloring problem on κ-claw free graphs. This models, for example, the scheduling of dependent jobs on multiple dedicated machines, where each job requires the exclusive use of a most κ machines. Assuming that κ is a fixed constant, we obtain the first constant factor approximation for the problem.

KW - Approximation algorithms

KW - Multicoloring

KW - Scheduling dependent jobs

KW - Sum coloring

UR - http://www.scopus.com/inward/record.url?scp=0242489508&partnerID=8YFLogxK

U2 - 10.1007/s00453-003-1031-8

DO - 10.1007/s00453-003-1031-8

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AN - SCOPUS:0242489508

SN - 0178-4617

VL - 37

SP - 187

EP - 209

JO - Algorithmica

JF - Algorithmica

IS - 3

ER -