An optimal sorting algorithm for mesh connected computers
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Lower bounds for sorting on mesh-connected architectures
Acta Informatica
Routing and sorting on mesh-connected arrays (extended abstract)
VLSI Algorithms and Architectures
Bounds for 1-selection and related problems on grids of processors
on Parcella '88: Fourth International Workshop on Parallel Processing by Cellular Automata and Arrays
Time lower bounds for sorting on multi-dimensional mesh-connected processor arrays
Information Processing Letters
Average case analysis of greedy routing algorithms on arrays
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Randomized sorting and selection on mesh-connected processor arrays (preliminary version)
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Balanced routing: towards the distance bound on grids
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
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
Indexing functions and time lower bounds for sorting on a mesh-connected computer
Discrete Applied Mathematics
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
Derandomizing algorithms for routing and sorting on meshes
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Sorting on a mesh-connected parallel computer
Communications of the ACM
Block Gossiping on Grids and Tori: Deterministic Sorting and Routing Match the Bisection Bound
ESA '93 Proceedings of the First Annual European Symposium on Algorithms
Universal schemes for parallel communication
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Computer organization and algorithms for very-high speed computations.
Computer organization and algorithms for very-high speed computations.
Matrix Transpose on Meshes: Theory and Practice
IPPS '97 Proceedings of the 11th International Symposium on Parallel Processing
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We show improved bounds for 1–1 routing and sorting on multi-dimensional meshes and tori. In particular, we give a fairly simple deterministic algorithm for sorting on the d-dimensional mesh of side length n that achieves a running time of 3dn/2+o(n) for the d-dimensional mesh and torus, respectively, that make one copy of each element. We also show lower bounds for sorting with respect to a large class of indexing schemes, under a model of the mesh where each processor can hold an arbitrary number of packets. Finally, we describe algorithms for permutation routing whose running times come very close to the diameter lower bound.