Abstract
We give a distributed algorithm that constructs a O(logn)- approximate minimum spanning tree (MST) in arbitrary networks. Our algorithm runs in time \(\tilde{O}(D(G) + L(G,w))\) 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 exists graphs which need Ω(D(G)+ L(G,w)) time to compute an H-approximation to the MST for any H ∈[1, Θ(logn)]. 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 optimal \(\tilde{O}(D(G))\) time.
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Khan, M., Pandurangan, G. (2006). A Fast Distributed Approximation Algorithm for Minimum Spanning Trees. In: Dolev, S. (eds) Distributed Computing. DISC 2006. Lecture Notes in Computer Science, vol 4167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11864219_25
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DOI: https://doi.org/10.1007/11864219_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44624-8
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