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Journal Articles Operations Research Letters Year : 2007

The maximum integer multiterminal flow problem in directed graphs

Cédric Bentz


This paper deals with the algorithmic aspects of one fundamental problem generalizing the famous maximum flow problem. This problem arises, in particular, as a requests routing problem in networks. Given an edge-capacitated graph and k terminal vertices, the maximum integer multiterminal flow problem (MaxIMTF) is to route the maximum number of flow units between the terminals. We study this problem in directed graphs and identify a key parameter, that was not considered previously: kL, the number of lonely terminals (a terminal is lonely if it lies on at least one directed cycle containing no other terminal). We prove that MaxIMTF is polynomial-time solvable when there is no lonely terminal and NP-hard to approximate within 2-? (for any ? 0), even when kL=1 and k=3 (and also when kL=k=2). We also give an (2 log (kL+2))-approximation algorithm for the general case, and show that the case kL=1 and k=2 is tractable. Moreover, some of our results for MaxIMTF extend to the well-known associated minimum multiterminal cut problem or match previous results known for this minimization problem.
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hal-01125132 , version 1 (06-03-2015)


  • HAL Id : hal-01125132 , version 1


Cédric Bentz. The maximum integer multiterminal flow problem in directed graphs. Operations Research Letters, 2007, 35, pp.195-200. ⟨hal-01125132⟩


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