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The Inapproximability of Maximum Single-Sink Unsplittable, Priority and Confluent Flow Problems [article]

F. Bruce Shepherd, Adrian Vetta
2015 arXiv   pre-print
Furthermore, we examine these maximisation problems for three specialised types of network flow: unsplittable, confluent and priority flows.  ...  In the confluent flow problem, we have node capacities, and the final flow must induce a tree. Both of these problems have been studied extensively, primarily in the single-sink setting.  ...  The authors thank Guyslain Naves for his careful reading and precise and helpful comments. The authors gratefully acknowledge support from the NSERC Discovery Grant Program.  ... 
arXiv:1504.00627v2 fatcat:i2fmgalrgfgh7hfsry4rnugk74

Network Flow Problems Arising From Evacuation Planning [article]

Daniel Dressler, Technische Universität Berlin, Technische Universität Berlin, Martin Skutella
We assume we are given a network of the area to be evacuated, with sources describing the locations of evacuees, and sinks describing safe areas.  ...  We discuss the effects of flow conservation for our generalized model, as well as the complexity of the associated transshipment problem under various settings.  ...  One can use MaxConf-Flow to model the decision version of their problem using a single sink s − , but their inapproximability within a factor of 1 2 log 2 |δ in (s − )|−ε does not carry over to the maximum  ... 
doi:10.14279/depositonce-3327 fatcat:ldwqwcb6e5hchbjstboirlq4gm