Tractable Parameterizations for the Minimum Linear Arrangement Problem

Michael R. Fellows, Danny Hermelin, Frances Rosamond, Hadas Shachnai

Research output: Contribution to journalArticlepeer-review


The MINIMUM LINEAR ARRANGEMENT (MLA) problem involves embedding a given graph on the integer line so that the sum of the edge lengths of the embedded graph is minimized. Most layout problems are either intractable or not known to be tractable, parameterized by the treewidth of the input graph. We investigate MLA with respect to three parameters that provide more structure than treewidth. In particular, we give a factor (1+ϵ)-approximation algorithm for MLA parameterized by (ϵ, k), where k is the vertex cover number of the input graph. By a similar approach, we obtain two FPT algorithms that exactly solve MLA parameterized by, respectively, the max leaf and edge clique cover numbers of the input graph.

Original languageAmerican English
Article number6
JournalACM Transactions on Computation Theory
Issue number2
StatePublished - 1 May 2016


  • Fixed parameter tractability
  • Parameterized algorithms

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computational Theory and Mathematics


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