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
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AN - SCOPUS:84860277505
SN - 1549-6325
VL - 8
JO - ACM Transactions on Algorithms
JF - ACM Transactions on Algorithms
IS - 2
M1 - 9
ER -