Improvements on the k-center problem for uncertain data

In real applications, there are situations where we need to model some problems based on uncertain data. This leads us to define an uncertain model for some classical geometric optimization problems and propose algorithms to solve them. In this paper, we study the k-center problem, for uncertain input. In our setting, each uncertain point Pi is located independently from other points in one of several possible locations {Pi,1, . . . , Pi,zi} in a metric space with metric d, with specified probabilities and the goal is to compute k-centers {c1, . . . , ck} that minimize the following expected cost Ecost(c1, . . . , ck) = ∑ R∈Ω prob(R) max i=1,...,n min j=1,...k d(P̂i, cj) here Ω is the probability space of all realizations R = {P̂1, . . . , P̂n} of given uncertain points and