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Generalized max flows and augmenting paths

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Book cover Integer Programming and Combinatorial Optimization (IPCO 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 920))

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Abstract

It is well-known that if augmenting paths are used to solve a max flow problem then two problems can arise: 1) the number of augmenting paths needed can depend on the size of the capacities; and 2) if the capacities are irrational then the algorithm need not even converge to an optimal solution. Edmonds and Karp [4] and Dinic [3] were the first to show that these problems can be overcome using minimum length augmenting paths. In this paper we examine to what extent augmenting paths and the results of Edmonds and Karp can be generalized. In particular, we consider these ideas for the following generalized max flow problem (first studied by Fulkerson [7]): maxx 1:Ax=0,0≤x≤c.

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Authors and Affiliations

  1. Department of Management, College of Business Administration, University of Notre Dame, 46556, Notre Dame, IN

    David Hartvigsen

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  1. David Hartvigsen
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Egon Balas Jens Clausen

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© 1995 Springer-Verlag Berlin Heidelberg

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Hartvigsen, D. (1995). Generalized max flows and augmenting paths. In: Balas, E., Clausen, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1995. Lecture Notes in Computer Science, vol 920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59408-6_51

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  • DOI: https://doi.org/10.1007/3-540-59408-6_51

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59408-6

  • Online ISBN: 978-3-540-49245-0

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