Journal ArticleDOI
Optimal routing algorithms for mesh-connected processor arrays
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TLDR
In this article, a randomized oblivious algorithm for routing any (partial) permutation on an ann?n grid in 2n + O(logn) parallel communication steps is presented, where the queues will not grow larger than log logn with high probability.Abstract:
We show that there is a randomizedoblivious algorithm for routing any (partial) permutation on ann ?n grid in 2n +O(logn) parallel communication steps. The queues will not grow larger than ź(logn/log logn) with high probability. We then modify this to obtain a (nonoblivious) algorithm with the same running time such that the size of the queues is bounded by a constant with high probability. For permutations withlocality, where each packet has to travel a distance at mostL, a generalization of the algorithm routes in time proportional toL with high probability. Finally, we identify a class of meshlike networks that have optimal or near-optimal diameter. These meshes have the potential of being adapted to run existing sorting and routing algorithms with corresponding reduction in their running times.read more
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Book ChapterDOI
General purpose parallel architectures
TL;DR: In this article, the authors focus on general purpose parallel architectures and propose the XPRAM with ρ processors, where each processor executes a number of local instructions and sends or receives some messages that implement global read or write instructions.
Journal ArticleDOI
Randomized routing and sorting on fixed-connection networks
TL;DR: In this paper, the authors present a general paradigm for the design of packet routing algorithms for fixed-connection networks, which is based on a randomized on-line algorithm for scheduling any set of N packets whose paths have congestion c on any bounded-degree leveled network with depth L in O(c + L + log N) steps, using constant-size queues.
Journal ArticleDOI
Packet Routing in Fixed-Connection Networks
TL;DR: This work focuses on (partial) permutation, k-relation routing, routing to random destinations, dynamic routing, isotonic routing, fault tolerant routing, and related sorting results.
Journal ArticleDOI
Randomized routing, selection, and sorting on the OTIS-mesh
TL;DR: This paper presents efficient algorithms for packet routing, sorting, and selection on the OTIS-Mesh and reveals that the queue size needed for these algorithms is O(1) with high probability.
Journal ArticleDOI
A 2nź2 step algorithm for routing in ann ×n array with constant-size queues
TL;DR: A deterministic algorithm for solving any 1–1 packet-routing problem on ann ×n mesh in 2n−2 steps using constant-size queues and the time bound is optimal in the worst case.
References
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Design of a Massively Parallel Processor
TL;DR: The massively parallel processor (MPP) as discussed by the authors was designed to process satellite imagery at high rates, achieving 8-bit integer data, addition can occur at 6553 million operations per second (MOPS) and multiplication at 1861 MOPS.
Proceedings ArticleDOI
Universal schemes for parallel communication
Leslie G. Valiant,G. J. Brebner +1 more
TL;DR: This paper shows that there exists an N-processor computer that can simulate arbitrary N- processor parallel computations with only a factor of O(log N) loss of runtime efficiency, and isolates a combinatorial problem that lies at the heart of this question.
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A scheme for fast parallel communication
TL;DR: There is a distributed randomized algorithm that can route every packet to its destination without two packets passing down the same wire at any one time, and finishes within time $O(\log N)$ with overwhelming probability for all such routing requests.
Journal ArticleDOI
Sorting on a mesh-connected parallel computer
C. D. Thompson,Hsiang-Tsung Kung +1 more
TL;DR: Two algorithms are presented for sorting n2 elements on an n × n mesh-connected processor array that require O (n) routing and comparison steps and are shown to be optimal in time within small constant factors.
Journal ArticleDOI
Data broadcasting in SIMD computers
David Nassimi,Sartaj Sahni +1 more
TL;DR: Considers the data broadcasting problem for single instruction stream, multiple data stream (SIMD) computers and two versions of this problem, i.e., random access read (RAR) and random access write (RAW) are considered.