An overview of representative problems in location research
Management Science
A linear-time algorithm for concave one-dimensional dynamic programming
Information Processing Letters
Dynamic and static algorithms for optimal placement of resources in a tree
Theoretical Computer Science
A Simple Linear Time Algorithm for Concave One-Dimensional Dynamic Programming
A Simple Linear Time Algorithm for Concave One-Dimensional Dynamic Programming
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Journal of Computer and System Sciences
An O(pn2) algorithm for the p -median and related problems on tree graphs
Operations Research Letters
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The p-center problem is to locate p facilities on a network so as to minimize the largest distance from a demand point to its nearest facility. the p-median problem is to locate p facilities on a network so as to minimize the average distance from one of the n demand points to one of the p facilities. We provide, given the interval model of an n vertex interval graph, an O(n) time algorithm for the 1-median problem on the interval graph. We also show how to solve the p-median problem, for arbitrary p, on an interval graph in O(pn log n) time and on an circular-arc graph in O(pn2 log n) time. other than for trees, no polynomial time algorithm for p-median problem has been reported for any large class of graphs. We introduce a spring model of computation and show how to solve the p-center problem on an circular-arc graph in O(pn) time, assuming that the arc endpoints are sorted.