TY - JOUR

T1 - Dotted interval graphs

AU - Aumann, Yonatan

AU - Lewenstein, Moshe

AU - Melamud, Oren

AU - Pinter, Ron

AU - Yakhini, Zohar

PY - 2012/4

Y1 - 2012/4

N2 - We introduce a generalization of interval graphs, which we call Dotted Interval Graphs (DIG). A dotted interval graph is an intersection graph of arithmetic progressions (dotted intervals). Coloring of dotted interval graphs naturally arises in the context of high throughput genotyping. We study the properties of dotted interval graphs, with a focus on coloring. We show that any graph is a DIG, but that DIGd graphs, that is, DIGs in which the arithmetic progressions have a jump of at most d, form a strict hierarchy. We show that coloring DIG d graphs is NP-complete even for d = 2. For any fixed d, we provide a 5/6d + o(d) approximation for the coloring of DIG d graphs. Finally, we show that finding the maximal clique in DIG d graphs is fixed parameter tractable in d.

AB - We introduce a generalization of interval graphs, which we call Dotted Interval Graphs (DIG). A dotted interval graph is an intersection graph of arithmetic progressions (dotted intervals). Coloring of dotted interval graphs naturally arises in the context of high throughput genotyping. We study the properties of dotted interval graphs, with a focus on coloring. We show that any graph is a DIG, but that DIGd graphs, that is, DIGs in which the arithmetic progressions have a jump of at most d, form a strict hierarchy. We show that coloring DIG d graphs is NP-complete even for d = 2. For any fixed d, we provide a 5/6d + o(d) approximation for the coloring of DIG d graphs. Finally, we show that finding the maximal clique in DIG d graphs is fixed parameter tractable in d.

KW - Approximation algorithms

KW - Circular arc graph

KW - Graph coloring

KW - Graph theory

KW - Intersection graph

KW - Interval graph

UR - http://www.scopus.com/inward/record.url?scp=84860277505&partnerID=8YFLogxK

U2 - 10.1145/2151171.2151172

DO - 10.1145/2151171.2151172

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84860277505

SN - 1549-6325

VL - 8

JO - ACM Transactions on Algorithms

JF - ACM Transactions on Algorithms

IS - 2

M1 - 9

ER -