## 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 DIG_{d} graphs, i.e. DIGs in which the arithmetic progressions have a jump of at most d, form a strict hierarchy. We show that coloring DIG_{d} graphs is NP-complete even for d = 2. For any fixed d, we provide a 7/8d approximation for the coloring of DIG_{d} graphs.

Original language | English |
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Pages | 339-348 |

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

Conference | Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms |
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Country/Territory | United States |

City | Vancouver, BC |

Period | 23/01/05 → 25/01/05 |