no. 2
A polynomial algorithm for minDSC on a subclass of series parallel graphs
RAIRO - Operations Research - Recherche Opérationnelle, Tome 43 (2009) no. 2, pp. 145-156.

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.

DOI : 10.1051/ro/2009009
Classification : 05C78, 05C85, 90B35
Mots clés : minimum directed sumcut, series parallel graph, polynomial algorithm 
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     author = {Achouri, Salim and Bossart, Timoth\'ee and Munier-Kordon, Alix},
     title = {A polynomial algorithm for {minDSC} on a subclass of series parallel graphs},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {145--156},
     publisher = {EDP-Sciences},
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     year = {2009},
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Achouri, Salim; Bossart, Timothée; Munier-Kordon, Alix. A polynomial algorithm for minDSC on a subclass of series parallel graphs. RAIRO - Operations Research - Recherche Opérationnelle, Tome 43 (2009) no. 2, pp. 145-156. doi : 10.1051/ro/2009009. http://www.numdam.org/articles/10.1051/ro/2009009/

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