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Algorithmica

, Volume 80, Issue 2, pp 714–741 | Cite as

Output-Polynomial Enumeration on Graphs of Bounded (Local) Linear MIM-Width

  • Petr A. Golovach
  • Pinar Heggernes
  • Mamadou Moustapha Kanté
  • Dieter Kratsch
  • Sigve H. Sæther
  • Yngve Villanger
Article

Abstract

The linear induced matching width (LMIM-width) of a graph is a width parameter defined by using the notion of branch-decompositions of a set function on ternary trees. In this paper we study output-polynomial enumeration algorithms on graphs of bounded LMIM-width and graphs of bounded local LMIM-width. In particular, we show that all 1-minimal and all 1-maximal \((\sigma ,\rho )\)-dominating sets, and hence all minimal dominating sets, of graphs of bounded LMIM-width can be enumerated with polynomial (linear) delay using polynomial space. Furthermore, we show that all minimal dominating sets of a unit square graph can be enumerated in incremental polynomial time.

Keywords

Domination problem Local linear MIM-width Output-polynomial enumeration Linear delay 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Petr A. Golovach
    • 1
  • Pinar Heggernes
    • 1
  • Mamadou Moustapha Kanté
    • 2
  • Dieter Kratsch
    • 3
  • Sigve H. Sæther
    • 1
  • Yngve Villanger
    • 1
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.LIMOS, CNRSUniversité Clermont AuvergneAubiéreFrance
  3. 3.LITAUniversité de LorraineMetzFrance

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