Permutations on Illiac IV-Type Networks
IEEE Transactions on Computers
A logarithmic time sort for linear size networks
Journal of the ACM (JACM)
An optimal sorting algorithm for mesh connected computers
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Array processor with multiple broadcasting
Journal of Parallel and Distributed Computing
A 2n-2 step algorithm for routing in an nxn array with constant size queues
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Meshes with reconfigurable buses
Proceedings of the fifth MIT conference on Advanced research in VLSI
Average case analysis of greedy routing algorithms on arrays
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Constant queue routing on a mesh
STACS 91 Proceedings of the 8th annual symposium on Theoretical aspects of computer science
Journal of Parallel and Distributed Computing
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Concentrated regular data streams on grids: sorting and routing near to the bisection bound
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Matching the bisection bound for routing and sorting on the mesh
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Optimal sorting on mesh-connected processor arrays
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
A randomized algorithm for multipacket routing on the mesh
Journal of Parallel and Distributed Computing
k-k routing, k-k sorting, and cut-through routing on the mesh
Journal of Algorithms
Histogramming on a Reconfigurable Mesh Computer
IPPS '92 Proceedings of the 6th International Parallel Processing Symposium
An Optimal Sorting Algorithm on Reconfigurable Mesh
IPPS '92 Proceedings of the 6th International Parallel Processing Symposium
Permutation Routing on Reconfigurable Meshes
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
Proceedings of the Tenth Conference on Foundations of Software Technology and Theoretical Computer Science
Mesh Connected Computers with Fixed and Reconfigurable Buses: Packet Routing, Sorting, and Selection
ESA '93 Proceedings of the First Annual European Symposium on Algorithms
Sorting by Parallel Insertion on a One-Dimensional Subbus Array
IEEE Transactions on Computers
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Mesh connected computers have become attractive models of computing because of their varied special features. In this paper we consider two variations of the mesh model: 1) a mesh with fixed buses, and 2) a mesh with reconfigurable buses. Both these models have been the subject matter of extensive previous research. We solve numerous important problems related to packet routing and sorting on these models. In particular, we provide lower bounds and very nearly matching upper bounds for the following problems on both these models: 1) Routing on a linear array; and 2) k驴k routing and k驴k sorting on a 2D mesh for any k驴 12. We provide an improved algorithm for 1 驴 1 routing and a matching sorting algorithm. In addition we present greedy algorithms for 1 驴 1 routing, k驴k routing, and k驴k sorting that are better on average and supply matching lower bounds. We also show that sorting can be performed in logarithmic time on a mesh with fixed buses. Most of our algorithms have considerably better time bounds than known algorithms for the same problems.