Improved algorithms for optimal k sink location on path networks

Abstract

We address the problem of placing k sinks on dynamic-flow path networks with n vertices so as to minimize their maximum evacuation completion time. We develop two different algorithms that, when all edges have the same capacity, run respectively in $O(n+k^2{\log }^{2}n)$ and $O(n\log n)$ time. When the edge capacities can be different, i.e., are general, they run respectively in $O(n\log n+k^2{\log }^{4}n)$ and $O(n{\log }^{3}n)$ time.

These algorithms improve upon the previously most efficient algorithms, which had time complexities $O\left(kn\right)$ and $O(kn{\log }^{2}n)$, respectively, for the uniform and general edge capacity models. The improvements are achieved by moving from a dynamic programming based approach to a parametric-search based one.