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Maximal Flow in Branching Trees and Binary Search Trees

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Abstract

A capacitated network is a tree with a non negative number, called capacity, associated to each edge. The maximal flow that can pass through a given path is the minimun capacity on the path. Antal and Krapivski (Phys Rev E 74:051110, 2006) study the distribution for the maximal flow from the root to a leaf in the case of a deterministic binary tree with independent and identically distributed random capacities. In this paper their result is extended to three classes of trees with a random number of children and dependent random capacities: binary trees with general capacities distribution, branching trees with exchangeable capacities and random binary search trees.

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Authors and Affiliations

  1. Department of Mathematics, University of Pavia, via Ferrata 1, 27100, Pavia, Italy

    Federico Bassetti

  2. Faculty of Economics, Universidad de Navarra, Campus Universitario, edificio de biblioteca (entrada este), 31080, Pamplona, Spain

    Fabrizio Leisen

Authors
  1. Federico Bassetti
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  2. Fabrizio Leisen
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Correspondence to Fabrizio Leisen.

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Bassetti, F., Leisen, F. Maximal Flow in Branching Trees and Binary Search Trees. Methodol Comput Appl Probab 13, 475–486 (2011). https://doi.org/10.1007/s11009-010-9164-0

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  • DOI: https://doi.org/10.1007/s11009-010-9164-0

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