Stupid Columnsort Tricks

Leighton’s columnsort algorithm sorts on an r × s mesh, subject to the restrictions that s is a divisor of r and that r ≥ 2s2 (so that the mesh is tall and thin). We show how to mitigate both of these restrictions. One result is that the requirement that s is a divisor of r is unnecessary; columnsort sorts correctly whether or not s divides r . We present two algorithms that, as long as s is a perfect square, relax the restriction that r ≥ 2s2; both reduce the exponent of s to 3/2. One algorithm requires r ≥ 4s3/2 if s divides r and r ≥ 6s3/2 if s does not divide r . The other algorithm requires r ≥ 43/2, and it requires s to be a divisor of r . Both algorithms have applications in increasing the maximum problem size in out-of-core sorting programs. This research was supported in part by NSF Grant EIA-98-02068.