The input/output complexity of sorting and related problems
Communications of the ACM
Tight bounds on the complexity of parallel sorting
IEEE Transactions on Computers
An introduction to parallel algorithms
An introduction to parallel algorithms
k-k routing, k-k sorting, and cut-through routing on the mesh
Journal of Algorithms
Better trade-offs for parallel list ranking
Proceedings of the ninth annual ACM symposium on Parallel algorithms and architectures
IEEE Transactions on Parallel and Distributed Systems
Derandomizing algorithms for routing and sorting on meshes
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Work-optimal simulation of PRAM models on meshes
Nordic Journal of Computing
Parallel Alternating-Direction Access Machine
MFCS '96 Proceedings of the 21st International Symposium on Mathematical Foundations of Computer Science
Practical Parallel List Ranking
IRREGULAR '97 Proceedings of the 4th International Symposium on Solving Irregularly Structured Problems in Parallel
Routing on the PADAM: Degrees of Optimality
Euro-Par '97 Proceedings of the Third International Euro-Par Conference on Parallel Processing
Euro-Par '97 Proceedings of the Third International Euro-Par Conference on Parallel Processing
List Ranking on Interconnection Networks
Euro-Par '96 Proceedings of the Second International Euro-Par Conference on Parallel Processing - Volume I
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
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
A parallel computer as a NOC region
Networks on chip
Performance comparison of some shared memory organizations for 2D mesh-like NOCs
Microprocessors & Microsystems
Address-free all-to-all routing in sparse torus
PaCT'07 Proceedings of the 9th international conference on Parallel Computing Technologies
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A sparse-mesh, which has PUs on the diagonal of a two-dimensional grid only, is a cost effective distributed memory machine. Variants of this machine have been considered before, but none are as simple and pure as a sparse-mesh. Various fundamental problems (routing, sorting, list ranking) are analyzed, proving that sparse-meshes have great potential. It is shown that on a two-dimensional $n \times n$ sparse-mesh, which has $n$ PUs, for $h = \omega(n^\epsilon \cdot \log n)$, h-relations can be routed in $(h + o(h)) / \epsilon$ steps. The results are extended for higher dimensional sparse-meshes. On a $d$-dimensional $n \times \cdots \times n$ sparse-mesh, with $h = \omega(n^\epsilon \cdot \log n)$, h-relations are routed in $(6 \cdot (d - 1) / \epsilon - 4) \cdot (h + o(h))$ steps.