Issue RAIRO-Oper. Res. Volume 43, Number 2, April-June 2009 Page(s) 145 - 156 DOI 10.1051/ro/2009009 Published online 28 April 2009

RAIRO-Oper. Res. 43 (2009) 145-156
DOI: 10.1051/ro/2009009

A polynomial algorithm for minDSC on a subclass of series Parallel graphs

Salim Achouri, Timothée Bossart and Alix Munier-Kordon

LIP6 - Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 05, France; Alix.Munier@lip6.fr

Received June 30, 2007. Accepted July 3, 2008. Published online 28 April 2009

Abstract
The aim of this paper is to show a polynomial algorithm for the problem minimum directed sumcut for a class of series parallel digraphs. The method uses the recursive structure of parallel compositions in order to define a dominating set of orders. Then, the optimal order is easily reached by minimizing the directed sumcut. It is also shown that this approach cannot be applied in two more general classes of series parallel digraphs.

Mathematics Subject Classification. 05C78, 05C85, 90B35.

Key words: Minimum directed sumcut, series parallel graph, polynomial algorithm.


© EDP Sciences, ROADEF, SMAI 2009

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