Proceedings ArticleDOI
On bit-serial packet routing for the mesh and the torus
Fillia Makedon,A. Simvonis +1 more
- pp 294-302
TLDR
A new lower bound is derived for distance-limited permutation routing on a ring of processors, and an algorithm that matches this lower bound if the packets are routed independently is given.Abstract:
The bit-serial routing problem wherein each packet consists of a sequence of k flits and is thus called a snake, is considered. On the basis of the properties of the snake during the routing, a formal definition is given for three different packet routing models, namely, the store-and-forward model, the cut-through model, and the wormhole model. The wormhole model, which is most commonly used in practice, is studied. The first algorithms (deterministic and probabilistic) based on the wormhole model for the permutation routing problem on a chain, on a square mesh, and on a square torus are given. A new lower bound is derived for distance-limited permutation routing on a ring of processors, and an algorithm that matches this lower bound if the packets are routed independently is given. >read more
Citations
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Proceedings ArticleDOI
A theory of wormhole routing in parallel computers
TL;DR: Simulation results suggest that the idea of random initial delays is not only useful for theoretical analysis but may actually improve the performance of wormhole routing algorithms.
Proceedings ArticleDOI
Matching the bisection bound for routing and sorting on the mesh
TL;DR: This paper presents randomized algorithms for kk routing, k-k sorting, and cut through routing on the mesh connected processor array and these algorithms have optimal queue length, namely k + o(k).
Journal ArticleDOI
k-k routing, k-k sorting, and cut-through routing on the mesh
TL;DR: Kn /2 is a known lower bound for all three problems (which is the bisection bound), and hence the algorithms are very nearly optimal.
Journal ArticleDOI
A theory of wormhole routing in parallel computers
TL;DR: This paper gives theoretical analyses of simple wormhole routing algorithms, showing them to be nearly optimal for butterfly and mesh connected networks, and reports simulation results suggesting that the idea of random initial delays may have an impact beyond theoretical analysis.
References
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Parviz Kermani,Leonard Kleinrock +1 more
TL;DR: The analysis shows that cut-through switching is superior (and at worst identical) to message switching with respect to the above three performance measures.
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The Torus Routing Chip
TL;DR: The torus routing chip (TRC) is a selftimed chip that performs deadlock-free cut-through routing ink-aryn-cube multiprocessor interconnection networks using a new method of deadlock avoidance called virtual channels.
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.
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.
Proceedings ArticleDOI
An optimal sorting algorithm for mesh connected computers
Claus-Peter Schnorr,Adi Shamir +1 more
TL;DR: A 3n upper and lower bound on the complexity of sorting on a n × n mesh connected parallel computer is proved and an exceptionally simple algorithm which sorts the array by alternately sorting its rows and columns log log n times is described.