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arXiv · 1605.02307

Combinatorial analysis of growth models for series-parallel networks

Markus Kuba·Alois Panholzer
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Abstract

We give combinatorial descriptions of two stochastic growth models for series-parallel networks introduced by Hosam Mahmoud by encoding the growth process via recursive tree structures. Using decompositions of the tree structures and applying analytic combinatorics methods allows a study of quantities in the corresponding series-parallel networks. For both models we obtain limiting distribution results for the degree of the poles and the length of a random source-to-sink path, and furthermore we get asymptotic results for the expected number of source-to-sink paths.

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Markus Kuba, Alois Panholzer. 2016-05-08. Combinatorial analysis of growth models for series-parallel networks. https://arxiv.org/abs/1605.02307

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