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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.
@article{RO_2009__43_2_145_0,
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},
volume = {43},
number = {2},
year = {2009},
doi = {10.1051/ro/2009009},
mrnumber = {2527860},
zbl = {1162.05349},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2009009/}
}
TY - JOUR AU - Achouri, Salim AU - Bossart, Timothée AU - Munier-Kordon, Alix TI - A polynomial algorithm for minDSC on a subclass of series parallel graphs JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2009 SP - 145 EP - 156 VL - 43 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ro/2009009/ DO - 10.1051/ro/2009009 LA - en ID - RO_2009__43_2_145_0 ER -
%0 Journal Article %A Achouri, Salim %A Bossart, Timothée %A Munier-Kordon, Alix %T A polynomial algorithm for minDSC on a subclass of series parallel graphs %J RAIRO - Operations Research - Recherche Opérationnelle %D 2009 %P 145-156 %V 43 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ro/2009009/ %R 10.1051/ro/2009009 %G en %F RO_2009__43_2_145_0
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
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