TY - JOUR

T1 - Tractable parameterizations for the MINIMUM LINEAR ARRANGEMENT problem

AU - Fellows, Michael R.

AU - Hermelin, Danny

AU - Rosamond, Frances

AU - Shachnai, Hadas

N1 - Publisher Copyright:
© 2016 ACM.

PY - 2016/5/1

Y1 - 2016/5/1

N2 - 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.

AB - 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.

KW - Fixed parameter tractability

KW - MINIMUM LINEAR ARRANGEMENT

KW - Parameterized algorithms

UR - http://www.scopus.com/inward/record.url?scp=84969963442&partnerID=8YFLogxK

U2 - 10.1145/2898352

DO - 10.1145/2898352

M3 - Article

AN - SCOPUS:84969963442

VL - 8

JO - ACM Transactions on Computation Theory

JF - ACM Transactions on Computation Theory

SN - 1942-3454

IS - 2

M1 - 6

ER -