Tractable parameterizations for the minimum linear arrangement problem

Michael R. Fellows; Danny Hermelin; Frances A. Rosamond; Hadas Shachnai

doi:10.1007/978-3-642-40450-4_39

Tractable parameterizations for the minimum linear arrangement problem

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

Ben-Gurion University of the Negev, Technion - Israel Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The Minimum Linear Arrangement (MLA) problem asks to embed 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 graphs. 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 describe two FPT algorithms that exactly solve MLA parameterized by, respectively, the max leaf and edge clique cover numbers of the input graph.

Original language	American English
Title of host publication	Algorithms, ESA 2013 - 21st Annual European Symposium, Proceedings
Pages	457-468
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-40450-4_39
State	Published - 24 Sep 2013
Event	21st Annual European Symposium on Algorithms, ESA 2013 - Sophia Antipolis, France Duration: 2 Sep 2013 → 4 Sep 2013

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8125 LNCS

Conference

Conference	21st Annual European Symposium on Algorithms, ESA 2013
Country/Territory	France
City	Sophia Antipolis
Period	2/09/13 → 4/09/13

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-40450-4_39

Cite this

Fellows, M. R., Hermelin, D., Rosamond, F. A., & Shachnai, H. (2013). Tractable parameterizations for the minimum linear arrangement problem. In Algorithms, ESA 2013 - 21st Annual European Symposium, Proceedings (pp. 457-468). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8125 LNCS). https://doi.org/10.1007/978-3-642-40450-4_39

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title = "Tractable parameterizations for the minimum linear arrangement problem",

abstract = "The Minimum Linear Arrangement (MLA) problem asks to embed 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 graphs. 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 describe two FPT algorithms that exactly solve MLA parameterized by, respectively, the max leaf and edge clique cover numbers of the input graph.",

author = "Fellows, {Michael R.} and Danny Hermelin and Rosamond, {Frances A.} and Hadas Shachnai",

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note = "21st Annual European Symposium on Algorithms, ESA 2013 ; Conference date: 02-09-2013 Through 04-09-2013",

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Fellows, MR, Hermelin, D, Rosamond, FA & Shachnai, H 2013, Tractable parameterizations for the minimum linear arrangement problem. in Algorithms, ESA 2013 - 21st Annual European Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8125 LNCS, pp. 457-468, 21st Annual European Symposium on Algorithms, ESA 2013, Sophia Antipolis, France, 2/09/13. https://doi.org/10.1007/978-3-642-40450-4_39

Tractable parameterizations for the minimum linear arrangement problem. / Fellows, Michael R.; Hermelin, Danny; Rosamond, Frances A. et al.
Algorithms, ESA 2013 - 21st Annual European Symposium, Proceedings. 2013. p. 457-468 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8125 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - The Minimum Linear Arrangement (MLA) problem asks to embed 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 graphs. 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 describe two FPT algorithms that exactly solve MLA parameterized by, respectively, the max leaf and edge clique cover numbers of the input graph.

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Fellows MR, Hermelin D, Rosamond FA, Shachnai H. Tractable parameterizations for the minimum linear arrangement problem. In Algorithms, ESA 2013 - 21st Annual European Symposium, Proceedings. 2013. p. 457-468. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-40450-4_39

Tractable parameterizations for the minimum linear arrangement problem

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All Science Journal Classification (ASJC) codes

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