Abstract
We study integral 2-commodity flows in networks with a special characteristic, namely symmetry. We show that the Symmetric 2-Commodity Flow Problem is in P, by proving that the cut criterion is a necessary and sufficient condition for the existence of a solution. We also give a polynomial-time algorithm whose complexity is 6 C flow + O (|A|), where C flow is the time complexity of your favorite flow algorithm (usually in O(|V| ×|A|)). Our result closes an open question in a surprising way, since it is known that the Integral 2-Commodity Flow Problem is NP-complete for both directed and undirected graphs. This work finds application in optical telecommunication networks.
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© 2004 Springer-Verlag Berlin Heidelberg
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Jarry, A. (2004). Integral Symmetric 2-Commodity Flows. In: Diekert, V., Habib, M. (eds) STACS 2004. STACS 2004. Lecture Notes in Computer Science, vol 2996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24749-4_36
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DOI: https://doi.org/10.1007/978-3-540-24749-4_36
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