Easy problems for tree-decomposable graphs
Journal of Algorithms
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Meet and merge: Approximation algorithms for confluent flows
Journal of Computer and System Sciences - Special issue on network algorithms 2005
(Almost) Tight bounds and existence theorems for single-commodity confluent flows
Journal of the ACM (JACM)
Capacitated confluent flows: complexity and algorithms
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
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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 in destination-based routing. We study the maximum confluent flow problem (MaxConf) with a single commodity but multiple sources and sinks and heterogeneous arc capacities. It was recently shown that MaxConf is NP-hard even on trees. We improve the classification of easy and hard confluent flow problems by providing polynomial-time algorithms for outerplanar graphs with a single sink, as well as trees with a constant number of either sources or sinks. Furthermore, we present an FPTAS for graphs with bounded treewidth.