New lower bounds for parallel computation
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Upper and lower time bounds for parallel random access machines without simultaneous writes
SIAM Journal on Computing
Optimal bounds for decision problems on the CRCW PRAM
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Relations between concurrent-write models of parallel computation
SIAM Journal on Computing
The parallel complexity of element distinctness is Ω(√log n)
SIAM Journal on Discrete Mathematics
A universal interconnection pattern for parallel computers
Journal of the ACM (JACM)
Relations between concurrent-write models of parallel computation
PODC '84 Proceedings of the third annual ACM symposium on Principles of distributed computing
Optimal parallel algorithms for string matching
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Efficient algorithms for multiple access channels
Efficient algorithms for multiple access channels
A complexity theory for unbounded fan-in parallelism
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Approximate and exact parallel scheduling with applications to list, tree and graph problems
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
An optimal randomized parallel algorithm for finding connected components in a graph
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Finding Biconnected Componemts And Computing Tree Functions In Logarithmic Parallel Time
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Parallel algorithms for separable permutations
Discrete Applied Mathematics
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We consider the relative power of concurrentwrite PRAMs when the number of processors (and input variables) is fixed at n, and infinite shared memory is allowed. Several different models (COMMON, ARBITRARY, PRIORITY) have been used for algorithm design in the literature; these models differ in their method of write-conflict resolution. Recent work in separating these models ([FRW1,2,3], [LY]) has relied on further restrictions (limiting the size of memory or the power of processors); the only unrestricted results known concern the element distinctness problem ([FMW], [RSSW]). In this paper we contribute further unrestricted results. We consider the COLLISION model, a natural generalization of the Ethernet ([G]). Our main result is a lower bound of Ω(logloglogn) steps on COLLISION for a problem that can be done in O(1) steps on ARBITRARY. We use this result, together with a reduction performed by means of Ramsey's Theorem, to show that the powers of COMMON and COLLISION are incomparable. We also introduce a new and natural model, TOLERANT, and show that it is strictly less powerful than COLLISION and incomparable with COMMON. The proofs involved use combinatorial arguments, including Turán's Theorem for graphs and the Erdös-Rado intersecting set theorem.