Minmax sink location problem on dynamic cycle networks

Abstract

We address both 1 and k sink location problems on dynamic cycle networks. Our 1-sink algorithms run in O(n) and O(nlogn) time for uniform and general edge capacity cases, respectively. We improve the previously best known O(nlogn) time algorithm for single sink introduced by Xu et al. [Xu et al. 2015] with uniform capacities. When k¿1, we improve two results [Benkoczi et al. 2017] for both with uniform and arbitrary capacities by a factor of O(logn). Using the same sorted matrices optimization framework originally devised by Frederickson and Johnson and employed by [Benkoczi et al. 2017], our algorithms for the k-sink problems have time complexities of O(nlogn) for uniform, and O(nlog3 n) for arbitrary capacities. Key to our results is a novel data structure called a cluster head forest, which allows one to compute batches of queries for evacuation time efficiently.