An improved algorithm for the distance constrained p-center location problem with mutual communication on tree networks

In a recent article Averbakh and Berman present an O(p ³√(log log p)(log p) + n²) serial algorithm to solve the distance constrained p-center location problem with mutual communication on a tree network with n nodes. In this note we suggest two simple modifications leading to the improved (subquadratic in n), O(p ³√(log log p)(log p) + p(n + p)log²(n + p)) complexity bound. We also present a new O(p²n log n log(n + p)) algorithm for the discrete version of this problem.