Invasion percolation and global optimization
Albert-L\'aszl\'o Barab\'as (Department of Physics, University of, Notre Dame)
TL;DR
This paper establishes a precise connection between invasion bond percolation and Prim's algorithm, introducing a new IBP model that generates minimal energy trees within the same universality class.
Contribution
It maps invasion bond percolation to Prim's algorithm and introduces a novel IBP model for minimal energy spanning trees, applicable across various dimensions and lattices.
Findings
Mapped IBP exactly to Prim's algorithm
Introduced a new IBP model with minimal energy trees
Model applicable to arbitrary dimensions and lattices
Abstract
Invasion bond percolation (IBP) is mapped exactly into Prim's algorithm for finding the shortest spanning tree of a weighted random graph. Exploring this mapping, which is valid for arbitrary dimensions and lattices, we introduce a new IBP model that belongs to the same universality class as IBP and generates the minimal energy tree spanning the IBP cluster.
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Taxonomy
TopicsTheoretical and Computational Physics · Complex Network Analysis Techniques · Stochastic processes and statistical mechanics