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.
|Number of pages||10|
|State||Published - 2005|
|Event||Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms - Vancouver, BC, United States|
Duration: 23 Jan 2005 → 25 Jan 2005
|Conference||Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms|
|Period||23/01/05 → 25/01/05|