The complexity of parallel sorting
The model the authors consider is the (concurrent-write, PRIORITY) PRAM. It has n synchronous processors, which communicate via an infinite shared memory. When several processors simultaneously write to the same cell, the one with the largest index succeeds. They allow the processors arbitrary computational power. The main result is that sorting n integers requires ..cap omega..(..sqrt..log n) steps in this strong model. This bound is proved in two stages. First, using a novel Ramsey theoretic argument, we ''reduce'' sorting on a PRAM to sorting on a parallel merge tree. This tree is a generalization of Valiant's parallel comparison tree from (V) in which at every step n pairs of (previously ordered) sets are merged (rather then n pairs of elements compared). The second stage is proving the lower bound for such trees. The Ramsey theoretic technique, together with known methods for bounding the ''degree'' of the computation, can be used to unify and generalize previous lower bounds for PRAM's. For example, they show that the computation of any symmetric polynomial (e.g. the sum or product) on n integers requires exactly log/sub 2/n steps.
- Research Organization:
- J.W. Goethe Universitat, Frankfurt
- OSTI ID:
- 6537775
- Journal Information:
- SIAM J. Comput.; (United States), Journal Name: SIAM J. Comput.; (United States) Vol. 16:1; ISSN SMJCA
- Country of Publication:
- United States
- Language:
- English
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