Dotted Interval Graphs and High Throughput Genotyping

Y. Aumann, M. Lewenstein, O. Melamud, R. Pinter, Z. Yakhini

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.
Original languageAmerican English
Title of host publicationsixteenth annual ACM-SIAM symposium on Discrete algorithms
StatePublished - 2005

Bibliographical note

Place of conference:Vancouver, BC, Canada


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