Mesh-Connected Computers with Multiple Buses

Meshes with Multiple Buses

Quentin F. Stout
Computer Science and Engineering, University of Michigan

Abstract: This paper considers a model of parallel computers, mesh computers with buses, where each bus provides a broadcasting capability to the processors connected to it.

We first disprove a published claim by showing that on a 2-dimensional mesh with a bus for each row, where each row must solve its own problem with data that is independent of all other rows, there are problems where the rows can cooperatively solve all subproblems faster than any single row can solve its own problem. A specific example is the "leftmost 1" problem: all processors have either a 0 or a 1, and the goal is for each processor to determine the leftmost processor in its row which has a 1. For an n x n mesh this can be solved in

Θ(n) time if no broadcasting is used,
Θ(n^1/2) time if each row uses only its own bus, and
Θ(n^1/3) time if the rows cooperate.

As a corollary we obtain efficient parallel algorithms for some graph problems.

We also consider the optimal layout of buses for a given dimension and number of buses per processor, where optimality is defined in terms of the time needed to simulate any other machine with the same constraints. Optimal or nearly optimal layouts are determined for each possible choice of dimension and number of buses per processor. These layouts are based on tree, pyramid, and orthogonal tree (mesh-of-tree) designs, and are superior to all previously suggested bus layouts.

Keywords: parallel computer, row broadcasting, row bus, mesh computer, cooperative problem solving, cooperative speedup, optimal stepwise simulation, minimum, component labeling, spanning forest, tree, pyramid, mesh-of-trees

Complete paper. This paper appears in Proc. 27th IEEE Symp. on Foundations of Computer Science (1986), pp. 264-273.

My related work in parallel computing

I've worked on several different models of mesh-connected computers with broadcasting:
- 1-dimensional mesh computers with broadcasting with one bus for the entire system.
- 2-dimensional mesh computers with broadcasting with one bus for the entire system.
- reconfigurable meshes, where the buses are created dynamically.
My papers in parallel computing and an overview of my research.
An explanation of parallel computing and a tutorial, Parallel Computing 101.