Minmax sink location problem on dynamic cycle networks

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

An optimal algorithm for the weighted backup 2-center problem on a tree

In this paper, we are concerned with the weighted backup 2-center problem on a tree. The backup 2-center problem is a kind of center facility location problem, in which one is asked to deploy two facilities, with a given probability to fail, in a network. Given that the two facilities do not fail simultaneously, the goal is to find two locations, possibly on edges, that minimize the expected value of the maximum distance over all vertices to their closest functioning facility. In the weighted setting, each vertex in the network is associated with a nonnegative weight, and the distance from vertex $u$ to $v$ is weighted by the weight of $u$. With the strategy of prune-and-search, we propose a linear time algorithm, which is asymptotically optimal, to solve the weighted backup 2-center problem on a tree.Comment: 14 pages, 4 figure