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...

• Type: Conference
• Year: 2001
• Where: ICALP
• Authors: Bernard Chazelle, Ronitt Rubinfeld, Luca Trevisan
• Keywords: Algorithms, Approximation Algorithms, ICALP 2001, Minimum Spanning Tree, Programming Languages