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

Abstract

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 $O(n + k^2\log ^2n)$ time and $O(n\log n)$ time, respectively. These algorithms together improve upon the previously most efficient algorithms, which have time complexities $O(kn\log ^2n)$ [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.

B. Bhattacharya — Partially supported by a Discovery Grant from NSERC of Canada

M.J. Golin — Partially supported by Hong Kong RGC GRF grant 16208415

Y. Higashikawa and N. Katoh — Supported by JSPS KAKENHI Grant-in-Aid for Young Scientists (B) (17K12641)

Y. Higashikawa — Supported by JST CREST (JPMJCR1402)