Cs 408 the Multibutter Blockiny Network Abhiram Ranade

We have been considering the problem of designing a non-blocking network, i.e. a network in which we can simultaneously connect every input i to an output (i) where can be any permutation. We considered two candidates for this: the Butter y and the Benes. On the Butter y we saw that for some permutations it was indeed possible to make all N connections, where N is the number of inputs, but for some others it was possible to connect only p N of the inputs to the required outputs. On the Benes, we found that the connections could be made for all . An important issue in designing such networks is the algorithm for setting up the connections. To solve the problem on the Benes network, we needed to solve a colouring problem. While the algorithm for this is simple, it is not distributed { essentially we need to have one computer know all of and calculate the paths, and send that con guration to the network. It is preferred, if instead, the input nodes (which have a limited amount of processing in them) can decide only how to establish connections locally, based on some local querying, i.e. each node coordinates with its neighbours to determine the path for the message it holds. Unfortunately, it doesnt seem that such a distributed algorithm is possible for the Benes network. The Multibutter y network[4] solves this problem and others. A variant of this which we will call the reduced multibutter y, will be seen to have the non-blocking property, i.e. disjoint paths can be established for any permutation . Further, the paths can be found using a distributed algorithm that runs in time O(logN). There exists a more complex O(logN) time algorithm as well, but we will not discuss this. Multibutter ies also possess some fault-tolerance properties, and a few other interesting properties which we will not study.