Improved Algorithms for Computing k-Sink on Dynamic Flow Path Networks.

We address the problem of locating k sinks on dynamic flow path networks with n vertices in such a way that the evacuation completion time to them is minimized. Our two algorithms run in O(n log n + k(2) log(4) n) and O(n log(3) n) time, respectively. When all edges have the same capacity, we also present two algorithms which run in O(n + k(2) log(2) n) time and O(n log n) time, respectively. These algorithms together improve upon the previously most efficient algorithms, which have time complexities O(kn log(2) n) [1] and O(kn) [11], in the general and uniform edge capacity cases, respectively. The above results are achieved by organizing relevant data for subpaths in a strategic way during preprocessing, and the final results are obtained by extracting/merging them in an efficient manner.