Optimization Problems in Dotted Interval Graphs

Dan Hermelin, Julián Mestre, Dror Rawitz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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 (Inf. Processing Letters, 98(1):29-33, 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.

Original languageEnglish GB
Title of host publicationGraph-Theoretic Concepts in Computer Science
Subtitle of host publication38th International Workshop, WG 2012, Revised Selected Papers
EditorsMartin Charles Golumbic, Michal Stern, Avivit Levy, Gila Morgenstern
Number of pages11
StatePublished - 2 Nov 2012
Externally publishedYes
Event38th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2012 - Jerusalem, Israel
Duration: 26 Jun 201228 Jun 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
ISSN (Print)0302-9743


Conference38th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2012

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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