
In this paper, we analyze the performance of parallel multithreaded algorithms that use dag-consistent distributed shared memory. Specifically, we analyze execution time, page faults, and space requirements for multithreaded algorithms executed by a workstealing thread scheduler and the BACKER algorithm for maintaining dag consistency. We prove that if the accesses to the backing store are random and independent (the BACKER algorithm actually uses hashing), the expected execution time TP(C) of a “fully strict” multithreaded computation on P processors, each with a LRU cache of C pages, is O(T1(C)=P+mCT∞), where T1(C) is the total work of the computation including page faults, T∞ is its critical-path length excluding page faults, and m is the minimum page transfer time. As a corollary to this theorem, we show that the expected number FP(C) of page faults incurred by a computation executed on P processors can be related to the number F1(C) of serial page faults by the formula FP(C) F1(C)+O(CPT∞). Finally, we give simple bounds on the number of page faults and the space requirements for “regular” divide-and-conquer algorithms. We use these bounds to analyze parallel multithreaded algorithms for matrix multiplication and LU-decomposition.
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