Circulations, Fuzzy Relations and Semirings

  • Roland Glück
  • Bernhard Möller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5133)


Circulations are similar to flows in capacity-constrained networks, with the difference that they also observe lower bounds and, unlike flows, are not directed from a source to a sink. We give a new description of circulations in networks using a technique introduced by Kawahara; he applied the same methods to network flows. We show the power and flexibility of his approach in a new application, refining it at the same time by introducing the concept of test relations. Furthermore we will give algebraic formulations of a generic algorithm for computing a flow in a network with lower bounds and a sufficient and necessary criterion for the existence of a circulation.


Lower Bound Inverse Semigroup Capacity Constraint Scalar Multiplication Network Flow 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Roland Glück
    • 1
  • Bernhard Möller
    • 1
  1. 1.Institut für InformatikUniversität AugsburgAugsburgGermany

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