Permutation Communication in All-Optical Rings.

We study the wavelength problem and arc (edge) congestion problem for communicatingpermutation instances on a ring. We prove that the numbers of wavelengthsin the directed case\Gamma!w , in the undirected case w, and the arc congestion\Gamma!? and theedge congestion ? for a permutation instance I 1 on an n-vertex ring C n satisfy:\Gamma!w (C n ; I 1 ) ?n3?;\Gamma!? (C n ; I 1 ) ?n4?;w(C n ; I 1 ) ?n2?; ?(C n ; I 1 ) ?￥n2:All bounds...