Correctness of Balanced Networks 318

We presented a new proof that the bitonic network is a counting network. Our proof consists of a routine veriication of the necessary and suucient conditions involved in combinatorial characterization theorems for counting and merging networks shown in 8]. This proof is a concrete instance of a paradigmatic methodology, suggested in this work, for showing correctness of balancing networks. For other instances where this methodology has already been applied and yielded corresponding proofs of comparable modularity and simplicity, we refer the reader to 7, 10]. It would yet be interesting to further investigate the generality of our proof technique by applying it to other constructions of counting networks. Good candidates would be the periodic counting network with fan-out 2 k 5] and the periodic smoothing network with fan-out p k 13]. Finally, recent randomized constructions of counting and smoothing networks 2], using randomized bal-ancers, call for corresponding methodologies for proving probabilistic properties of randomized constructions. (Research Project \Load Balancing Problems in Shared-Memory Multiprocessor Architectures"). We have had helpful discussions with Maurice Herlihy and Nancy Lynch on our initial ideas on investigating techniques for proving correctness of constructions of balancing networks, based on the theory developed in 8], in the context of a concrete example. Special thanks go to Mauricio Resende and an anonymous referee for many helpful editorial and wording comments.