COMPUTING THE 2-MEDIAN ON TREE NETWORKS IN O(N-LG-N) TIME

Location of facilities on tree networks is an important problem in transportation and telecommunication systems. For tree networks, the best-known algorithm to find 2-medians has a time complexity of O(n(2)). By exploiting the properties relating the I-median and the 2-medians in tree networks, and the properties inherent in tree structure, an improved algorithm is developed for computing the e-median. The time complexity of this algorithm is O(n lg n). The details of the algorithm are described along with an illustrative example. (C) 1995 John Wiley & Sons, Inc.