| Issue |
RAIRO-Oper. Res.
Volume 52, Number 4-5, October–December 2018
|
|
|---|---|---|
| Page(s) | 1123 - 1145 | |
| DOI | https://doi.org/10.1051/ro/2017011 | |
| Published online | 22 November 2018 | |
Lower and upper bounds for the linear arrangement problem on interval graphs
1
LIMOS, UMR CNRS 6158, LABEX IMOBS3, Université Blaise Pascal,
Clermont-Ferrand, France.
2
Département d’Informatique et de Mathématique, Université du Québec à Chicoutimi,
Saguenay,
QC G7H 2B1, Canada.
* Corresponding author: djamal.rebaine@uqac.ca
Received:
23
June
2015
Accepted:
2
March
2017
We deal here with the Linear Arrangement Problem (LAP) on interval graphs, any interval graph being given here together with its representation as the intersection graph of some collection of intervals, and so with related precedence and inclusion relations. We first propose a lower bound LB, which happens to be tight in the case of unit interval graphs. Next, we introduce the restriction PCLAP of LAP which is obtained by requiring any feasible solution of LAP to be consistent with the precedence relation, and prove that PCLAP can be solved in polynomial time. Finally, we show both theoretically and experimentally that PCLAP solutions are a good approximation for LAP on interval graphs.
Mathematics Subject Classification: 90C27
Key words: Interval Graphs / Linear Ordering
© EDP Sciences, ROADEF, SMAI 2018
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