Abstract
A flow on a directed network is said to be confluent if the flow uses at most one outgoing arc at each node. Confluent flows arise naturally from destination-based routing. We study the Maximum Confluent Flow Problem (MaxConf) with a single commodity but multiple sources and sinks. Unlike previous results, we consider heterogeneous arc capacities. The supplies and demands of the sources and sinks can also be bounded. We give a pseudo-polynomial time algorithm and an FPTAS for graphs with constant treewidth. Somewhat surprisingly, MaxConf is NP-hard even on trees, so these algorithms are, in a sense, best possible. We also show that it is NP-complete to approximate MaxConf better than 3/2 on general graphs.
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Dressler, D., Strehler, M. (2010). Capacitated Confluent Flows: Complexity and Algorithms. In: Calamoneri, T., Diaz, J. (eds) Algorithms and Complexity. CIAC 2010. Lecture Notes in Computer Science, vol 6078. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13073-1_31
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DOI: https://doi.org/10.1007/978-3-642-13073-1_31
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