One, two, three . . . infinity: lower bounds for parallel computation
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Optimal bounds for decision problems on the CRCW PRAM
Journal of the ACM (JACM)
An optimal O(log n)time parallel string matching algorithm
SIAM Journal on Computing
Every robust CRCW PRAM can efficiently simulate a PRIORITY PRAM
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Deterministic sampling—a new technique for fast pattern matching
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Converting high probability into nearly-constant time—with applications to parallel hashing
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
A lower bound for parallel string matching
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Fast hashing on a PRAM—designing by expectation
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Ultra-fast expected time parallel algorithms
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
A theorem on probabilistic constant depth Computations
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Optimal parallel construction of Hamiltonian cycles and spanning trees in random graphs
SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
An Ω(√ log log n) lower bound for routing in optical networks
SPAA '94 Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures
Computational bounds for fundamental problems on general-purpose parallel models
Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures
Fast deterministic processor allocation
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Optimal parallel approximation for prefix sums and integer sorting
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Approximate Compaction and Padded-Sorting on Exclusive Write PRAMs
IPPS '96 Proceedings of the 10th International Parallel Processing Symposium
Distribution-sensitive algorithms
Nordic Journal of Computing
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In order to obtain very fast parallel algorithms, it is almost always necessary to have some sort of load balancing procedure, so that processors which have finished their required tasks can help processors which have not. If the overloaded processors are not helped, then the expected time of the entire algorithm suffers. In general, we would like to distribute the remaining work as evenly as possible among the processors, or more formally, given at most n independent tasks distributed in an arbitrary way among n processors, we would like to redistribute the tasks so that each processor contains O(1) tasks. We show here that even on the strongest randomized CRCW PRAM model, for a simple random distribution tasks load balancing requires &OHgr;(log* n) expected time. Gil, Matias, and Vishkin [9] give an O(log* n) expected time randomized algorithm which solves the load balancing problem in the worst case, so the lower bound is tight.By reduction we show that both Padded Sort [12], and Linear Approximate Compaction [13] require &OHgr;(log* n) expected time. We note that our basic technique is one of the few parallel lower bound techniques known which only require 0/1 inputs. We also note that the bounds given in this paper do not place any restriction on the instruction set of the machine, the amount of information which can be stored in a memory cell, or on the number of memory cells.