The minimum shared edges problem on grid-like graphs

Till Fluschnik, Meike Hatzel, Steffen Härtlein, Hendrik Molter, Henning Seidler

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

2 Scopus citations


We study the NP -hard Minimum Shared Edges (MSE) problem on graphs: decide whether it is possible to route p paths from a start vertex to a target vertex in a given graph while using at most k edges more than once. We show that MSE can be decided on bounded (i.e. finite) grids in linear time when both dimensions are either small or large compared to the number p of paths. On the contrary, we show that MSE remains NP -hard on subgraphs of bounded grids. Finally, we study MSE from a parametrised complexity point of view. It is known that MSE is fixed-parameter tractable with respect to the number p of paths. We show that, under standard complexity-theoretical assumptions, the problem parametrised by the combined parameter k, p, maximum degree, diameter, and treewidth does not admit a polynomial-size problem kernel, even when restricted to planar graphs.

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 43rd International Workshop, WG 2017, Revised Selected Papers
EditorsGerhard J. Woeginger, Hans L. Bodlaender
PublisherSpringer Verlag
Number of pages14
ISBN (Print)9783319687049
StatePublished - 1 Jan 2017
Externally publishedYes
Event43rd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2017 - Eindhoven, Netherlands
Duration: 21 Jun 201723 Jun 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10520 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference43rd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2017

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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