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Optimal lower bounds for some distributed algorithms for a complete network of processors
Theoretical Computer Science
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SIAM Journal on Computing
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Distributed computing: a locality-sensitive approach
A Distributed Algorithm for Minimum-Weight Spanning Trees
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A Near-Tight Lower Bound on the Time Complexity of Distributed MST Construction
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Distributed approximation: a survey
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SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
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Computer Networks: The International Journal of Computer and Telecommunications Networking
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APWeb/WAIM '09 Proceedings of the Joint International Conferences on Advances in Data and Web Management
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Algorithms and theory of computation handbook
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IEEE/ACM Transactions on Networking (TON)
Learning automata-based algorithms for solving stochastic minimum spanning tree problem
Applied Soft Computing
The Journal of Supercomputing
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International Journal of Sensor Networks
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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.