The cache complexity of multithreaded cache oblivious algorithms

We present a technique for analyzing the number of cache misses incurred by multithreaded cache oblivious algorithms on an idealized parallel machine in which each processor has a private cache. We specialize this technique to computations executed by the Cilk workstealing scheduler on a machine with dag-consistent shared memory. We show that a multithreaded cache oblivious matrix multiplication incurs O(n3 / √ Z +(Pn)1/3 n2 ) cache misses when executed by the Cilk scheduler on a machine with P processors, each with a cache of size Z, with high probability. This bound is tighter than previously published bounds. We also present a new multithreaded cache oblivious algorithm for 1D stencil computations incurring O(n2 /Z + n + √ Pn3+ǫ) cache misses with high probability, one for Gaussian elimination and back substitution, and one for the length computation part of the longest common subsequence problem incurring O n2 /Z + √ Pn3.58 cache misses with high probability.

• Type: Conference
• Year: 2006
• Where: SPAA
• Authors: Matteo Frigo, Volker Strumpen
• Keywords: Cache Misses, Cache Oblivious Algorithm, Distributed And Parallel Computing, Multithreaded Cache, SPAA 2006