Resource requirements for field programmable interconnection chips

In this paper we prove an Ω(n log n) lower bound on the number of edges of an n-permutation graph G=(V, E). The lower bound is applicable to and characterizes permutations for Field Programmable Interconnection Chips and, more importantly, permutation networks in general. We also propose a family of permutation networks as a variation of the known Benes network with a wide range of diameters, a network property directly related to routing delays. Finally, the relation between the total number of programmable switches and the routing delay (maximum length of routing paths for specific I/O permutations) is explored