Volume 126, Number 2, April 2019
|Number of page(s)||7|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||30 May 2019|
Statistical mechanics of bipartite z-matchings
1 Department of Statistics, University of Oxford - Oxford OX1 3LB, UK
2 School of Mathematical Sciences, Queen Mary University of London - London E1 4NS, UK
3 Alan Turing Institute, The British Library - London, UK
Received: 7 February 2019
Accepted: 25 April 2019
The matching problem has a large variety of applications including the allocation of competitive resources and network controllability. The statistical mechanics approach based on the cavity method has shown to be exact in characterising this combinatorial problem on locally tree-like networks. Here we use the cavity method to solve the many-to-one bipartite z-matching problem that can be considered to be a model for the characterisation of the capacity of user-server networks such as wireless communication networks. Finally we study the phase diagram of the model defined in network ensembles.
PACS: 89.75.Hc – Networks and genealogical trees / 89.75.-k – Complex systems / 64.60.-i – General studies of phase transitions
© EPLA, 2019
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