Dotted interval graphs and high throughput genotyping

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

Dotted interval graphs and high throughput genotyping

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

Department of Computer Science and Artificial Intelligence

Bar-Ilan University
Technion-Israel Institute of Technology

Research output: Contribution to conference › Paper › peer-review

11 Scopus citations

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
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
Country/Territory	United States
City	Vancouver, BC
Period	23/01/05 → 25/01/05

Cite this

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title = "Dotted interval graphs and high throughput genotyping",

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.",

author = "Yonatan Aumann and Moshe Lewenstein and Oren Melamud and Pinter, \{Ron Y.\} and Zohar Yakhini",

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AU - Lewenstein, Moshe

AU - Melamud, Oren

AU - Pinter, Ron Y.

AU - Yakhini, Zohar

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

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T2 - Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms

Y2 - 23 January 2005 through 25 January 2005

ER -

Dotted interval graphs and high throughput genotyping

Abstract

Conference

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