Computational limitations of small-depth circuits
Computational limitations of small-depth circuits
Relations between concurrent-write models of parallel computation
SIAM Journal on Computing
General purpose parallel architectures
Handbook of theoretical computer science (vol. A)
ISCA '91 Proceedings of the 18th annual international symposium on Computer architecture
Parallel Algorithms for Image Processing on OMC
IEEE Transactions on Computers
Load balancing requires &OHgr;(log*n) expected time
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Efficient optical communication in parallel computers
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Simple, efficient shared memory simulations
SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
Size-depth trade-offs for threshold circuits
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
On contention resolution protocols and associated probabilistic phenomena
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Direct Bulk-Synchronous Parallel Algorithms
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
Lower bounds for randomized exclusive write PRAMs
Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures
Applying randomized edge coloring algorithms to distributed communication: an experimental study
Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures
On multiprocessor system scheduling
Proceedings of the eighth annual ACM symposium on Parallel algorithms and architectures
Communication-processor tradeoffs in limited resources PRAM
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
Parallel I/O scheduling using randomized, distributed edge coloring algorithms
Journal of Parallel and Distributed Computing
Lower Bounds for Randomized Exclusive Write PRAMs
Theory of Computing Systems
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Optical communication is likely to significantly speed up parallel computation because the vast bandwidth of the optical medium can be divided to produce communication networks of very high degree. However, the problem of contention in high-degree networks makes the routing problem in these networks theoretically (and practically) difficult. In this paper we examine Valiant's h-relation routing problem, which is a fundamental problem in the theory of parallel computing. The h-relation routing problem arises both in the direct implementation of specific parallel algorithms on distributed-memory machines and in the general simulation of shared memory models such as the PRAM on distributed-memory machines. In an h -relation routing problem each processor has up to h messages that it wishes to send to other processors and each processor is the destination of at most h messages. We present a lower bound for routing an h-relation (for any h 1) on a complete optical network of size n. Our lower bound applies to any randomized distributed algorithm for this task. Specifically. we show that the expected number of communication steps required to route an arbitrary h-relation is Wh+loglogn . This is the first known lower bound for this problem which does not restrict the class of algorithms under consideration.