@MISC{00sublineartime, author = {}, title = {Sublinear Time Algorithms for Metric Space Problems}, year = {2000} }

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Abstract

Abstract In this paper we give approximation algorithms for the following problems on metric spaces: Furthest Pair, k-median, Minimum Routing Cost Spanning Tree, Multiple Sequence Alignment, Maximum Traveling Salesman Problem, Maximum Spanning Tree and Average Distance. The key property of our algorithms is that their running times is linear in the number of points. As the full specification of an n-point metric space is of size \Theta (n2), the complexity of our algorithms is sublinear with respect to the input size. All previous algorithms (exact or approximate) for these problems have running times \Omega (n2). We believe that our techniques can be applied to get similar bounds for other problems.