Efficient algorithms for centers and medians in interval and circular-arc graphsAbstract: 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 consider these problems when the network can be modelled by an interval or circular-arc graph. 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(pn^{2} log n) time. We introduce a spring model of the objective function 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. @article{bbkks-eacm-02 , author = "S. Bespamyatnikh and B. Bhattacharya and M. Keil and D. Kirkpatrick and M. Segal" , title = "Efficient algorithms for centers and medians in interval and circular-arc graphs" , journal = "Networks" , volume = 33 , number = 3 , year = 2002 , pages = "144-152" } |