Algorithms and average time bounds of sorting on a mesh-connected computer

We give three new parallel sorting algorithms on a mesh-connected computer with wraparound connections (i.e. a torus). These three algorithms, with the minimum queue size of 1, sort n² random input data items into a blocked snakelike row major order, a row major order, and a snakelike row major order, in 1.5n+o(n), 2n+o(n), and 2n+o(n) average steps, respectively. These results improve the previous results of 2n+o(n), 2.5n+o(n), and 2.5n+o(n), respectively. In addition, we prove that the distance bound n on a torus is an average-time lower bound independent of indexing schemes of sorting random input data items on it