Circulations, Fuzzy Relations and Semirings

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.