Abstract
Let T be a tree with n vertices. Consider the problem of finding a maximal flow from the leaves of T to the root with minimal cost. An O(nlogn)-algorithm is presented which solves this problem if the cost function is linear. Furthermore recent complexity results for generalizations of this problem obtained by replacing the objectice function by a separable convex function and/or the tree structure by a series-parallel graph are summarized.
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© 1984 Springer-Verlag Berlin Heidelberg
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Brucker, P. (1984). An O (nlogn)-Algorithm for the Minimum Cost Flow Problem in Trees. In: Hammer, G., Pallaschke, D. (eds) Selected Topics in Operations Research and Mathematical Economics. Lecture Notes in Economics and Mathematical Systems, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45567-4_22
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DOI: https://doi.org/10.1007/978-3-642-45567-4_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12918-9
Online ISBN: 978-3-642-45567-4
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