## Parallel Sorting in Two-Dimensional VLSI Models of Computation

- Isaac D. Scherson, Sandeep Sen
- IEEE Trans. Computers
- 1989

- Published 2015

Distributed Sorting " Indeed, I believe that virtually every important aspect of programming arises somewhere in the context of sorting [and searching]! " – Donald E. Knuth, The Art of Computer Programming In this chapter we study a classic problem in computer science—sorting— from a distributed computing perspective. In contrast to an orthodox single-processor sorting algorithm, no node has access to all data, instead the to-be-sorted values are distributed. Distributed sorting then boils down to: Definition 4.1 (Sorting). We choose a graph with n nodes v 1 ,. .. , v n. Initially each node stores a value. After applying a sorting algorithm, node v k stores the k th smallest value. Remarks: • What if we route all values to the same central node v, let v sort the values locally, and then route them to the correct destinations?! According to the message passing model studied in the first few chapters this is perfectly legal. With a star topology sorting finishes in O(1) time! Definition 4.2 (Node Contention). In each step of a synchronous algorithm, each node can only send and receive O(1) messages containing O(1) values, no matter how many neighbors the node has. To get a better intuitive understanding of distributed sorting, we start with two simple topologies, the array and the mesh. Let us begin with the array: 33

@inproceedings{2015bulletUD,
title={@bullet Using Definition 4.2 Sorting on a Star Graph Takes Linear Time. 4.1 Array & Mesh},
author={},
year={2015}
}