Load balancing in counter-rotated SONET rings

Load-balanced routing in SONET rings has attracted much attention recently. Most prior works model the SONET rings as undirected rings and the traffic as undirected chords. While this model fits well to the traditional telephony applications, it is inefficient for the explosive Internet traffic and multimedia data communications, which exhibit unidirectional and asymmetric nature. For these applications, it is proper to model the SONET rings as a pair of counter-rotated rings and the traffic as directed chords. In this paper we first explore general flow properties in counter-rotated rings, and then introduce flow rounding and unsplitting techniques. Afterwards an optimal integral routing algorithm is provided. Finally, we show the NP-completeness of optimal unsplit routing, and present several polynomial-time approximation algorithms