Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. David W. Matula

Second Advisor

Dr. Gary Chartrand

Third Advisor

Dr. John Petro

Fourth Advisor

Dr. Dalia Motzkin


The maximum concurrent flow (MCFP) is a generalized commodity flow problem, where every pair of entities can send and receive flow Ma85 , BM86 , MS86 . We develop efficient labeling algorithms to solve the MCFP. We explore the combinatorial structure of the MCFP and show that the problem of associating costs (distances) to the edges so as to maximize the minimum cost of routing the concurrent flow is the dual of the MCFP. This duality covers max-flow min-cut theorem as a special case. Applications in packet switched networks At81 and cluster analysis Ma86 are discussed.

Access Setting

Dissertation-Open Access

Included in

Mathematics Commons