Unit interval editing is fixed-parameter tractable

Research output: Chapter in book / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review

12 Citations (Scopus)


Given a graph G and integers k1, k2, and k3, the unit interval editing problem asks whether G can be transformed into a unit interval graph by at most k1 vertex deletions, k2 edge deletions, and k3 edge additions. We give an algorithm solving the problem in 2O(klogk) ·(n+m) time, where k:= k1 +k2 +k3, and n, m denote respectively the numbers of vertices and edges of G. Therefore, it is fixed-parameter tractable parameterized by the total number of allowed operations. This implies the fixed-parameter tractability of the unit interval edge deletion problem, for which we also present a more efficient algorithm running in time O(4k · (n + m)). Another result is an O(6k · (n + m))-time algorithm for the unit interval vertex deletion problem, significantly improving the best-known algorithm running in time O(6k · n6).
Original languageEnglish
Title of host publicationAutomata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783662476710
Publication statusPublished - 1 Jan 2015
Event42nd International Colloquium on Automata, Languages and Programming, ICALP 2015 - Kyoto, Japan
Duration: 6 Jul 201510 Jul 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference42nd International Colloquium on Automata, Languages and Programming, ICALP 2015

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

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