## Giovanni Manzini - Lower bounds for sparse matrix vector multiplication on hypercubic networks

dmtcs:249 - Discrete Mathematics & Theoretical Computer Science, January 1, 1998, Vol. 2 - https://doi.org/10.46298/dmtcs.249
Lower bounds for sparse matrix vector multiplication on hypercubic networks

Authors: Giovanni Manzini

In this paper we consider the problem of computing on a local memory machine the product y = Ax,where A is a random n×n sparse matrix with Θ (n) nonzero elements. To study the average case communication cost of this problem, we introduce four different probability measures on the set of sparse matrices. We prove that on most local memory machines with p processors, this computation requires Ω ((n/p) \log p) time on the average. We prove that the same lower bound also holds, in the worst case, for matrices with only 2n or 3n nonzero elements.

Volume: Vol. 2
Published on: January 1, 1998
Imported on: March 26, 2015
Keywords: bisection width lower bounds,Sparse matrices,pseudo expanders,hypercubic networks,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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