The p-maxian problem on interval graphs

Authors:
Yukun Cheng;Liying Kang
Affiliations:
Department of Mathematics, Shanghai University, Shanghai 200444, China and School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018, China;Department of Mathematics, Shanghai University, Shanghai 200444, China
Venue:
Discrete Applied Mathematics
Year:
2010

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Abstract

This paper deals with the p-maxian problem on interval graphs where each interval has a positive weight. First we propose a linear time algorithm which is similar to the algorithm of Bespamyatnikh for the unweighted 1-median problem on interval graphs to solve the weighted 1-maxian problem. For a 2-maxian problem, we show that two intervals with the minimum right endpoint and the maximum left endpoint, respectively, are an optimal solution. It can be easily extended to the p-maxian problem (p=3).