Advanced Collective Communication in WDM Optical Rings.

In this paper we give approximation algorithms for computing routing schemes and wavelength assignments (coloring) for some highly structured sets of communication requests on all optical undirected rings. In our setting, the nodes of the ring are divided into two disjoint classes. In the Internal-All-to-All problem each node sends a message to all the other nodes of the class it belongs. In the External-All-to-All problem each node sends a message to all the nodes of the other class. We prove that Internal-All-to-All instances can be efficiently and optimally routed and colored. For External-All-to-All instances we give an approximation algorithm which uses a number of colors that is at most 53 times the network congestion of the ring, where the network congestion is a lower bound on the optimal solution. Finally, we propose a heuristic technique for External-All-to-All instances. Our experimental results show that our heuristic provides good solutions on the average (6% off the optimum). 1. Computer Science Department, University of Bologna. Email: margara@cs.unibo.it 2. Computer Science Department, University of Chicago. Email: simon@cs.uchicago.edu 3. Computer Science Department, University of Bologna. Email: vassura@cs.unibo.it