2024/12/03 by Haitao Xu, Xu, Haitao, Jingru Zhang +1 · 1 citation
Computer Science · #Data Management and Algorithms #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences
paper · pdf · doi:10.48550/arxiv.2412.02559
openalex publication_date 2024/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the two-center problem on cactus graphs in facility locations, which aims to place two facilities on the graph network to serve customers in order to minimize the maximum transportation cost. In our problem, the location of each customer is uncertain and may appear at O(m) points on the network with probabilities. More specifically, given are a cactus graph G and a set \calP of n (weighted) uncertain points where every uncertain point has O(m) possible locations on G each associated with a probability and is of a non-negative weight. The problem aims to compute two centers (points) on G so that the maximum (weighted) expected distance of the n uncertain points to their own expected closest center is minimized. No previous algorithms are known for this problem. In this paper, we present the first algorithm for this problem and it solves the problem in O(|G|+ m2n2log mn) time.