Finding the conditional location of a median path on a tree

Authors:
Biing-Feng Wang;Tzu-Chin Lin;Chien-Hsin Lin;Shan-Chyun Ku
Affiliations:
Department of Computer Science, National Tsing Hua University, Hsinchu 30043, Taiwan, ROC;Department of Computer Science, National Tsing Hua University, Hsinchu 30043, Taiwan, ROC;Department of Computer Science, National Tsing Hua University, Hsinchu 30043, Taiwan, ROC;Department of Computer Science, National Tsing Hua University, Hsinchu 30043, Taiwan, ROC
Venue:
Information and Computation
Year:
2008

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Abstract

In this paper, we study the problem of locating a median path of limited length on a tree under the condition that some existing facilities are already located. The existing facilities may be located at any subset of vertices. Upper and lower bounds are proposed for both the discrete and continuous models. In the discrete model, a median path is not allowed to contain partial edges. In the continuous model, a median path may contain partial edges. The proposed upper bounds for these two models are O(nlogn) and O(nlogn@a(n)), respectively. They improve the previous known bounds from O(nlog^2n) and O(n^2), respectively. The proposed lower bounds are both @W(nlogn).