Time lower bounds for parallel sorting on a mesh-connected processor array

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We prove that (1+√6/2)n ≈ 2.22n is a time lower bound independent of indexing schemes for sorting n2 items on an n × n mesh-connected processor array. We distinguish between indexing schemes by showing that there exists an indexing scheme which is provably worse than the snake-like row-major indexing for sorting. We also derive lower bounds for various indexing schemes. All these results are obtained by using the chain argument which we provide in this paper.