Abstract

We present deterministic sorting and routing algorithms for grids and tori with additional diagonal connections. For large loads (h 12), where each processor has at most h data packets in the beginning and in the end, the sorting problem can be solved in optimal hn=6+o(n) and hn=12+o(n) steps for grids and tori with diagonals, respectively. For smaller loads we present a new concentration technique that yields very fast algorithms for h ! 12. For a load of 1, the theoretically most interesting case, sorting takes only 1:2n + o(n) steps and routing only 1:1n + o(n) steps. For tori we can present optimal algorithms for all loads h 1. The above algorithms all use a constant size memory for all processors and never copy or split packets. If packets may be copied, 1--1 sorting can be done in only in 2 3 n + o(n) on a torus with diagonals. Gaining in general a speedup of 3 by only doubling the number of communication links compared to a grid without diagonals, our work suggests to build ...

Citations