Better Necessary Conditions for Rearrangeably

We derive necessary conditions for the d-ary multilog switching networks to be f -cast rearrangeably nonblocking when the input stage does not have fanout capability, with and without crosstalk-free constraint. In electronic switching networks, connection routes cannot share a link but they can share a switching node. This is the case when there is no crosstalkfree constraint. In optical switching networks, it is often desirable to enforce the crosstalk-free constraint which forbids connection routes to share switching nodes. The most novel contribution of this paper is the analytical technique, which addresses the problem from an algebraic angle. Our necessary conditions are much better than previously known conditions. Moreover, our results are on general d-ary multi-log networks, while known results are on 2-ary networks only.