Lattice flows in networks

Lattice flows in networks We consider flows in networks analogous to numerical flows but such that values of arc capacities are elements of a lattice. We present an analog of the max-flow min-cut theorem. However, finding the value of the maximum flow for lattice flows is based on not this theorem but computations in the algebra of matrices over the lattice; in particular, the maximum flow value is found with the help of transitive closure of flow capacity functions. We show that there exists a correspondence between flows and solutions of special-form systems of linear equations over distributive lattices. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Lattice flows in networks

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Publisher
Pleiades Publishing
Copyright
Copyright © 2016 by Pleiades Publishing, Inc.
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S003294601601004X
Publisher site
See Article on Publisher Site

Abstract

We consider flows in networks analogous to numerical flows but such that values of arc capacities are elements of a lattice. We present an analog of the max-flow min-cut theorem. However, finding the value of the maximum flow for lattice flows is based on not this theorem but computations in the algebra of matrices over the lattice; in particular, the maximum flow value is found with the help of transitive closure of flow capacity functions. We show that there exists a correspondence between flows and solutions of special-form systems of linear equations over distributive lattices.

Journal

Problems of Information TransmissionSpringer Journals

Published: May 8, 2016

References

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