Estimating the weight of metric minimum spanning trees in sublinear-time

In this paper we present a sublinear time (1+ )-approximation randomized algorithm to estimate the weight of the minimum spanning tree of an n-point metric space. The running time of the algorithm is O(n/ O(1) ). Since the full description of an n-point metric space is of size (n2 ), the complexity of our algorithm is sublinear with respect to the input size. Our algorithm is almost optimal as it is not possible to approximate in o(n) time the weight of the minimum spanning tree to within any factor. Furthermore, it has been previously shown that no o(n2 ) algorithm exists that returns a spanning tree whose weight is within a constant times the optimum. Research supported in part by NSF grants CCR-0313219 and CCR-0105701, DFG grant Me 872/8-2, and IST program of the EU under contract IST-1999-14186 (ALCOM-FT). This is a preliminary, author's version of a paper to appear in STOC'04, c 2004 Association for Computing Machinery, Inc. It is posted here by permission of ACM for ...

• Type: Conference
• Year: 2004
• Where: STOC
• Authors: Artur Czumaj, Christian Sohler
• Keywords: Algorithms, Minimum Spanning Tree, N-point Metric Space, Nsf Grants Ccr-0313219, STOC 2004