Some parallel sorts on a mesh-connected processor array and their time efficiency
Journal of Parallel and Distributed Computing
Sorting in c log n parallel steps
Combinatorica
Tight bounds on the complexity of parallel sorting
IEEE Transactions on Computers
The periodic balanced sorting network
Journal of the ACM (JACM)
Average case analysis of five two-dimensional bubble sorting algorithms
SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
2d-bubblesorting in average time O(√N lg N)*
SPAA '94 Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Periodic Constant Depth Sorting Networks
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
GI - 13. Jahrestagung
Classifying Matrices Separating Rows and Columns
IEEE Transactions on Parallel and Distributed Systems
Fun-sort--or the chaos of unordered binary search
Discrete Applied Mathematics - Fun with algorithms 2 (FUN 2001)
Research note: Networks for sorting multitonic sequences
Journal of Parallel and Distributed Computing
Hi-index | 0.01 |
We consider comparator networks M that are used repeatedly: while the output produced by M is not sorted, it is fed again into M. Sorting algorithms working in this way are called periodic. The number of parallel steps performed during a single run of M is called its period, the sorting time of M is the total number of parallel steps that are necessary to sort in the worst case. Periodic sorting networks have the advantage that they need little hardware (control logic, wiring, area) and that they are adaptive. We are interested in comparator networks of a constant period, due to their potential applications in hardware design. Previously, very little was known on such networks. The fastest solutions required time O(n&egr;) where the depth was roughly 1/&egr;. We introduce a general method called periodification scheme that converts automatically an arbitrary sorting network that sorts n items in time T(n) and that has layout area A(n) into a sorting network that has period 5, sorts ***(n • T(n) items in time O(T()• log n), and has layout area O(A(n)) • T(n)). In particular, applying this scheme to Batcher's algorithms, we get practical period 5 comparator networks that sort in time O(log3n). For theoretical interest, one may use the AKS netork resulting in a period 5 comparator network with runtime O(log2n).