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

Chi Ho Yeung*, K.Y. Michael Wong, Bo Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number062805
Number of pages14
JournalPhysical Review E
Issue number6
Publication statusPublished - 10 Jun 2014

Bibliographical note

©2014 American Physical Society


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