We present a distributed algorithm that constructs an O(log n)-approximate minimum spanning tree (MST) in any arbitrary network. This algorithm runs in timeÕ(D(G)+ L(G, w)) where L(G, w) is a parameter called the local shortest path diameter and D(G) is the (unweighted) diameter of the graph. Our algorithm is existentially optimal (up to polylogarithmic factors), i.e., there exist graphs which need Ω(D(G) + L(G, w)) time to compute an H -approximation to the MST for any H ∈ [1, Θ(log n)]. Our result also shows that there can be a significant time gap between exact and approximate MST computation: there exists graphs in which the running time of our approximation algorithm is exponentially faster than the time-optimal distributed algorithm that computes the MST. Finally, we show that our algorithm can be used to find an approximate MST in wireless networks and in random weighted networks in almost optimalÕ(D(G)) time.
Khan and Pandurangan REF showed that there can be an exponential time gap between exact and approximate MST construction by showing that there exist graphs where any distributed (exact) MST algorithm takes Ω( √ n/ log n) rounds, whereas an O (log n)-approximate MST can be computed in O (log n) rounds.
A fast distributed approximation algorithm for minimum spanning trees
Distributed Computing
Distributed Computing
Computer Science Mathematics Engineering