The Maximum Integer Multiterminal Flow Problem

  • Cédric Bentz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3982)


Given an edge-capacitated graph and kterminal vertices, the maximum integer multiterminal flow problem (MaxIMTF) is to route the maximum number of flow units between the terminals. For directed graphs, we introduce a new parameter k L k and prove that MaxIMTF is \(\mathcal{NP}\)-hard when k = k L = 2 and when k L = 1 and k = 3, and polynomial-time solvable when k L = 0 and when k L = 1 and k = 2. We also give an 2 log2 (k L + 2)-approximation algorithm for the general case. For undirected graphs, we give a family of valid inequalities for MaxIMTF that has several interesting consequences, and show a correspondence with valid inequalities known for MaxIMTF and for the associated minimum multiterminal cut problem.


Approximation Algorithm Undirected Graph Valid Inequality Terminal Vertex Maximum Integer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Cédric Bentz
    • 1
  1. 1.CEDRIC-CNAMParis Cedex 03France

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