Bounds on the performance of message routing heuristics

Let S be a set of messages to be routed on an N×N omega network. In addition, suppose that S contains communication conflicts. One strategy to deal with such conflicts is to partition S into some number of subsets, called rounds, such that each subset is conflict-free. The messages are then routed through the network by successively routing the messages in each subset. The minimum round partitioning problem is the problem of partitioning a given message set into a minimum number of rounds. The author establishes upper and lower bounds on the performance ratio for two heuristics for partitioning message patterns into rounds. For both of these heuristics they give upper and lower bounds of O (log N) and Ω(logN), respectively