Graph classes: a survey
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Dotted interval graphs and high throughput genotyping
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Optimization problems in multiple-interval graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithm for coloring of dotted interval graphs
Information Processing Letters
Approximating minimum coloring and maximum independent set in dotted interval graphs
Information Processing Letters
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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 DIGd graphs is NP-complete even for d = 2. For any fixed d, we provide a 5/6d + o(d) approximation for the coloring of DIGd graphs. Finally, we show that finding the maximal clique in DIGd graphs is fixed parameter tractable in d.