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ICALP
2001
Springer

Approximating the Minimum Spanning Tree Weight in Sublinear Time

8 years 11 months ago
Approximating the Minimum Spanning Tree Weight in Sublinear Time
We present a probabilistic algorithm that, given a connected graph G (represented by adjacency lists) of average degree d, with edge weights in the set {1, . . . , w}, and given a parameter 0 < ε < 1/2, estimates in time O(dwε−2 log dw ε ) the weight of the minimum spanning tree (MST) of G with a relative error of at most ε. Note that the running time does not depend on the number of vertices in G. We also prove a nearly matching lower bound of Ω(dwε−2) on the probe and time complexity of any approximation algorithm for MST weight. The essential component of our algorithm is a procedure for estimating in time O(dε−2 log d ε ) the number of connected components of an unweighted graph to within an additive error of εn. (This becomes O(ε−2 log 1 ε ) for d = O(1).) The time bound is shown to be tight up to within the log d ε factor. Our connected-components algorithm picks O(1/ε2) vertices in the graph and then grows “local spanning trees” whose sizes are spe...
Bernard Chazelle, Ronitt Rubinfeld, Luca Trevisan
Added 29 Jul 2010
Updated 29 Jul 2010
Type Conference
Year 2001
Where ICALP
Authors Bernard Chazelle, Ronitt Rubinfeld, Luca Trevisan
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