A linear programming duality approach to analyzing strictly nonblocking d-ary multilog networks under general crosstalk constraints

Abstract

In an optical crossconnect architecture, two routes sharing a common switching element suffer from crosstalk. Vaez and Lea [16] introduced a parameter c which is the maximum number of distinct switching elements a route can share with other routes in the crossconnect. We present a new method of analyzing strictly nonblocking d-ary multilog networks under this general crosstalk constraint using linear programming duality. We improve known results on several fronts: (a) our sufficient conditions are better than known sufficient conditions for log d (N,0,m) to be nonblocking under the general crosstalk constraint, (b) our results are on d-ary multilog networks while known results are on binary networks, and (c) for several ranges of the parameter c, we give the first known necessary conditions for this problem which also match our sufficient conditions from the LP-duality approach. © 2008 Springer-Verlag Berlin Heidelberg.