Dotted interval graphs and high throughput genotyping

  • Authors:

  • Yonatan Aumann;Moshe Lewenstein;Oren Melamud;Ron Y. Pinter;Zohar Yakhini

  • Affiliations:

  • Bar-Ilan University, Ramat Gan, Israel;Bar-Ilan University, Ramat Gan, Israel;Bar-Ilan University, Ramat Gan, Israel;Technion, Israel;Agilent Laboratories, Technion, Haifa, Israel

  • Venue:
  • SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
  • Year:
  • 2005

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Abstract

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.