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• W3090834346 abstract "We present COPSIM a parallel implementation of standard integer multiplication for the distributed memory setting, and COPK a parallel implementation of Karatsuba's fast integer multiplication algorithm for a distributed memory setting. When using $mathcal{P}$ processors, each equipped with a local non-shared memory, to compute the product of tho $n$-digits integer numbers, under mild conditions, our algorithms achieve optimal speedup of the computational time. That is, $mathcal{O}left(n^2/mathcal{P}right)$ for COPSIM, and $mathcal{O}left(n^{log_2 3}/mathcal{P}right)$ for COPK. The total amount of memory required across the processors is $mathcal{O}left(nright)$, that is, within a constant factor of the minimum space required to store the input values. We rigorously analyze the Input/Output (I/O) cost of the proposed algorithms. We show that their bandwidth cost (i.e., the number of memory words sent or received by at least one processors) matches asymptotically corresponding known I/O lower bounds, and their latency (i.e., the number of messages sent or received in the algorithm's critical execution path) is asymptotically within a multiplicative factor $mathcal{O}left(log^2_2 mathcal{P}right)$ of the corresponding known I/O lower bounds. Hence, our algorithms are asymptotically optimal with respect to the bandwidth cost and almost asymptotically optimal with respect to the latency cost." @default.
• W3090834346 created "2020-10-08" @default.
• W3090834346 creator A5033637373 @default.
• W3090834346 date "2020-09-30" @default.
• W3090834346 modified "2023-09-23" @default.
• W3090834346 title "Communication-Optimal Parallel Standard and Karatsuba Integer Multiplication in the Distributed Memory Model." @default.
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• W3090834346 hasPublicationYear "2020" @default.
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