Optimal Sorting Algorithms on Incomplete Meshes with Arbitrary Fault Patterns

In this paper, we propose simple and effi cient algorithms for sorting on incomplete meshes. No hardware redundancy is required and no assumption is made about the availability of a complete submesh. The proposed robust sorting algorithms are very effi cient when only a few processors are faulty and degrade gracefully as the number of faults increases. In particular, we show that 1-1 sorting (1 key per healthy processor) in row-major or snakelike row-major order can be performed in 3n+o(n) communication and comparison steps on an n \Theta n incomplete mesh that has an arbitrary pattern of o( p n) faulty processors. This is the fastest algorithm reported thus far for sorting in row-major and snakelike row-major orders on faulty meshes and the time complexity is quite close to its lower bound. 1 Introduction A d-dimensional mesh consists of n 1 n 2 \Delta \Delta \Delta n d processors of degree 2d arranged in an n 1 \Theta n 2 \Theta n 3 \Theta \Delta \Delta \Delta \Theta n d grid. Wh..