Mesh connected computers with fixed and reconfigurable buses: packet routing and sorting

Abstract

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 − k routing and k − k sorting on a 2D mesh for any k ≥ 12. We provide an improved algorithm for 1 − 1 routing and a matching sorting algorithm. In addition we present greedy algorithms for 1 − 1 routing, k − k routing, and k − k sorting that are better on average and supply matching lower bounds. We also show that sorting can be performed * This research was supported in part by an NSF Research Initiation Award CCR-92-09260. Preliminary versions of some of the results in this paper were presented in the First Annual European Symposium on Algorithms, 1993. 1 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.

Packet Routing in Fixed-Connection Networks: A Survey

“…For meshes with buses, sorting is only slightly more complex than routing, since the buses are excellent for rapid broadcasting and gathering. Routing has been investigated in [140,188,261,301].…”

A two-pass exact algorithm for selection on Parallel Disk Systems

“…Examples of randomized parallel selection algorithms are: 1) Constant time algorithms on the comparison tree model [7], [8] that are based on the ideas from [6]; 2) Constant time maximum selection algorithms on the CRCW PRAM [9]; 3) Algorithms for the star graph [10]; 4) Algorithms for the hypercube [11]; and 5) Algorithms on the mesh [12], [13]. [14], [15] give a survey on randomized selection algorithms.…”

The Mesh With Binary Tree Networks: An Enhanced Mesh With Low Bus-Loading

“…To circumvent this problem, while building on the advantages of the mesh, researchers have proposed meshes enhanced with buses. The literature abounds with such models (for example, [2,3,5,6,12,15,16,23,26,27]) and results for them. Enhanced mesh models also capture the structure of many reconfigurable architectures and devices [33].…”