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
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:0242489508
SN - 0178-4617
VL - 37
SP - 187
EP - 209
JO - Algorithmica
JF - Algorithmica
IS - 3
ER -