Hypercubic Sorting Networks

Hypercubic sorting networks are a class of comparator networks whose structure maps e ciently to the hypercube and any of its bounded degree variants. Recently, n-input hypercubic sorting networks with depth 2O( plglg n) lgn have been discovered. These networks are the only known sorting networks of depth o(lg2 n) that are not based on expanders, and their existence raises the question of whether a depth of O(lgn) can be achieved by any hypercubic sorting network. In this paper, we resolve this question by establishing an ?lgnlglg n lg lglg n lower bound on the depth of any n-input hypercubic sorting network. Our lower bound can be extended to certain restricted classes of non-oblivious sorting algorithms on hypercubic machines.

• Type: Journal
• Year: 1998
• Where: SIAMCOMP
• Authors: Frank Thomson Leighton, C. Greg Plaxton
• Keywords: Comparator Networks, Hypercubic Sorting Network, Known Sorting Networks, SIAMCOMP 1998