Delayed path coupling and generating random permutations via distributed stochastic processes
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Contention resolution with constant expected delay
Journal of the ACM (JACM)
Bounded fan-out multimessage multicasting
Nordic Journal of Computing
Work-optimal simulation of PRAM models on meshes
Nordic Journal of Computing
How Helpers Hasten h-Relations
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Gossiping and broadcasting versus computing functions in networks
Discrete Applied Mathematics - Special issue on international workshop on algorithms, combinatorics, and optimization in interconnection networks (IWACOIN '99)
Adversarial contention resolution for simple channels
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
IEEE Transactions on Parallel and Distributed Systems
Contention resolution with heterogeneous job sizes
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Thinning protocols for routing h-relations over shared media
Journal of Parallel and Distributed Computing
The Journal of Supercomputing
ISPA'05 Proceedings of the Third international conference on Parallel and Distributed Processing and Applications
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In this paper, we consider the problem of interprocessor communication on parallel computers that have optical communication networks. We consider the completely connected optical-communication parallel computer (OCPC), which has a completely connected optical network, and also the mesh-of-optical-buses parallel computer (MOB-PC), which has a mesh of optical buses as its communication network. The particular communication problem that we study is that of realizing an h-relation. In this problem, each processor has at most h messages to send and at most h messages to receive. It is clear that any 1-relation can be realized in one communication step on an OCPC. However, the best previously known p-processor OCPC algorithm for realizing an arbitrary h-relation for h 1 requires $\Theta(h + \log p)$ expected communication steps. (This algorithm is due to Valiant and is based on earlier work of Anderson and Miller.) Valiant's algorithm is optimal only for $h=\Omega(\log p)$, and it is an open question of Geréb-Graus and Tsantilas whether there is a faster algorithm for h=o(log p). In this paper, we answer this question in the affirmative and we extend the range of optimality by considering the case in which $h\leq \log p$. In particular, we present a $\Theta(h + \log\log p)$-communication-step randomized algorithm that realizes an arbitrary h-relation on a p-processor OCPC. We show that if $h\leq \log p$, then the failure probability can be made as small as $p^{-\alpha}$ for any positive constant $\alpha$. We use the OCPC algorithm as a subroutine in a $\Theta(h + \log\log p)$-communication-step randomized algorithm that realizes an arbitrary h-relation on a $p\times p$-processor MOB-PC. Once again, we show that if $h\leq \log p$, then the failure probability can be made as small as $p^{-\alpha}$ for any positive constant $\alpha$.