The Probabilistic k-Center Problem

The k-Center problem on a graph is to nd a set K of k vertices minimizing the radius dened as the maximum distance between any vertex and K. We propose a probabilistic combinatorial optimization model for this problem, with uncertainty on vertices. This model is inspired by a wildre management problem. The graph represents the adjacency of zones of a landscape, where each vertex represents a zone. We consider a nite set of re scenarios with related probabilities. Given a k-center, its radius may change in some scenarios since some evacuation paths become impracticable. The objective is to nd a robust k-center that minimizes the expected value of the radius over all scenarios. We study this new problem with scenarios limited to a single burning vertex. First results deal with explicit solutions on paths and cycles, and hardness on planar graphs.