Dotted interval graphs and high throughput genotyping
Yonatan Aumann, Moshe Lewenstein, Oren Melamud, Ron Y. Pinter, Zohar Yakhini · 2005
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 intervals 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, i.e. DIGs in which the arithmetic progressions have a jump of at most d, form a strict hierarchy. We show that coloring DIGd graphs is NP-complete even for d = 2. For any fixed d, we provide a 7 8d approximation for the coloring of DIGd graphs.