Combinatorial analysis of growth models for series-parallel networks
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.
Keywords
Cite
@article{arxiv.1605.02307,
title = {Combinatorial analysis of growth models for series-parallel networks},
author = {Markus Kuba and Alois Panholzer},
journal= {arXiv preprint arXiv:1605.02307},
year = {2018}
}
Comments
One of the proceedings-papers of the conference AofA 2016: 27th International conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, Krakow, Poland, July 4-8, 2016