Coverage versus supply cost in facility location:physics of frustrated spin systems

Yeung, Chi Ho, Wong, K.Y. Michael and Li, Bo (2014). Coverage versus supply cost in facility location:physics of frustrated spin systems. Physical Review E, 89 (6),

Abstract

A comprehensive coverage is crucial for communication, supply, and transportation networks, yet it is limited by the requirement of extensive infrastructure and heavy energy consumption. Here, we draw an analogy between spins in antiferromagnet and outlets in supply networks, and apply techniques from the studies of disordered systems to elucidate the effects of balancing the coverage and supply costs on the network behavior. A readily applicable, coverage optimization algorithm is derived. Simulation results show that magnetized and antiferromagnetic domains emerge and coexist to balance the need for coverage and energy saving. The scaling of parameters with system size agrees with the continuum approximation in two dimensions and the tree approximation in random graphs. Due to frustration caused by the competition between coverage and supply cost, a transition between easy and hard computation regimes is observed. We further suggest a local expansion approach to greatly simplify the message updates which shed light on simplifications in other problems.

Publication DOI: https://doi.org/10.1103/PhysRevE.89.062805
Divisions: Engineering & Applied Sciences > Mathematics
Uncontrolled Keywords: Statistics and Probability,Condensed Matter Physics,Statistical and Nonlinear Physics
Full Text Link: http://reposito ... rd/1783.1-61435
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
Published Date: 2014-06-10
Authors: Yeung, Chi Ho
Wong, K.Y. Michael
Li, Bo

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