TY - JOUR

T1 - Optimization problems in dotted interval graphs

AU - Hermelin, Danny

AU - Mestre, Julián

AU - Rawitz, Dror

PY - 2014/9/10

Y1 - 2014/9/10

N2 - The class of D-dotted interval (d-DI) graphs is the class of intersection graphs of arithmetic progressions with jump (common difference) at most d. We consider various classical graph-theoretic optimization problems in d-DI graphs of arbitrarily, but fixed, d. We show that Maximum Independent Set, Minimum Vertex Cover, and Minimum Dominating Set can be solved in polynomial time in this graph class, answering an open question posed by Jiang (2006). We also show that Minimum Vertex Cover can be approximated within a factor of (1+ε), for any ε>0, in linear time. This algorithm generalizes to a wide class of deletion problems including the classical Minimum Feedback Vertex Set and Minimum Planar Deletion problems. Our algorithms are based on classical results in algorithmic graph theory and new structural properties of d-DI graphs that may be of independent interest.

AB - The class of D-dotted interval (d-DI) graphs is the class of intersection graphs of arithmetic progressions with jump (common difference) at most d. We consider various classical graph-theoretic optimization problems in d-DI graphs of arbitrarily, but fixed, d. We show that Maximum Independent Set, Minimum Vertex Cover, and Minimum Dominating Set can be solved in polynomial time in this graph class, answering an open question posed by Jiang (2006). We also show that Minimum Vertex Cover can be approximated within a factor of (1+ε), for any ε>0, in linear time. This algorithm generalizes to a wide class of deletion problems including the classical Minimum Feedback Vertex Set and Minimum Planar Deletion problems. Our algorithms are based on classical results in algorithmic graph theory and new structural properties of d-DI graphs that may be of independent interest.

KW - Deletion problems

KW - Dominating set

KW - Dotted interval graphs

KW - Independent set

KW - Vertex cover

UR - http://www.scopus.com/inward/record.url?scp=84902247846&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2014.04.014

DO - 10.1016/j.dam.2014.04.014

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AN - SCOPUS:84902247846

SN - 0166-218X

VL - 174

SP - 66

EP - 72

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -