In this paper we study a facility location problem in the form of transportation network. Based on the cavity method developed in statistical physics, we derive a message passing (MP) algorithm for solving this problem. Moreover, we develop an MP guided decimation strategy to facilitate convergence of the algorithm in loopy networks. Optimal locations of facilities in tilted square lattices and the corresponding scaling behaviours in different regimes are also discussed.
|Publication status||Published - Dec 2015|