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Spanning tree modulus for secure broadcast games
Author(s) -
Albin Nathan,
Kottegoda Kapila,
PoggiCorradini Pietro
Publication year - 2020
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.21945
Subject(s) - spanning tree , modulus , interpretation (philosophy) , probabilistic logic , graph , minimum spanning tree , mathematics , theoretical computer science , combinatorics , computer science , mathematical optimization , artificial intelligence , geometry , programming language
Abstract The theory of p ‐modulus provides a general framework for quantifying the richness of a family of objects on a graph. When applied to the family of spanning trees, p ‐modulus has an interesting probabilistic interpretation. In particular, the 2‐modulus problem in this case has been shown to be equivalent to the problem of finding a probability distribution on spanning trees that utilizes the edges of the graph as fairly as possible. In the present work, we use this fact to produce a game‐theoretic interpretation of modulus by employing modulus to solve a secure broadcast game.