The complexity of sorting on distributed systems
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Lower Bounds on Information Transfer in Distributed Computations
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Information Transfer in Distributed Computing with Applications to VLSI
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Distributed elections in an archimedean ring of processors
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Optimal fault-tolerant embedding of paths in twisted cubes
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Optimal Embeddings of Paths with Various Lengths in Twisted Cubes
IEEE Transactions on Parallel and Distributed Systems
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Bit complexity of breaking and achieving symmetry in chains and rings
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IEEE/ACM Transactions on Networking (TON)
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The main result of this paper is a general technique for determining lower bounds on the communication complexity of problems on various distributed computer networks. This general technique is derived by simulating the general network by a linear array and then using a lower bound on the communication complexity of the problem on the linear array. Applications of this technique yield optimal bounds on the communication complexity of merging, ranking, uniqueness, and triangle-detection problems on a ring of processors. Nontrivial near-optimal lower bounds on the communication complexity of distinctness, merging, and ranking on meshes and complete binary trees are also derived.