Distributed, Synchronized Implementation of an Algorithm for the Maximum Flow Problem

We present an implementation of the maximum flow algorithm of Shiloach and Vishkin (1982) on a distributed system without shared memory. This algorithm is a clever variation of Karzanov´s algorithm, has a clear parallel orientation, and possesses features which make it an interesting candidate for distributed implementation also. The paper briefly describes the algorithm and discusses implementation issues which are relevant regardless of the specifics of the distributed system at hand: distribution of data structures (graph, queue, stacks) and reduction of communication volume. Experiments with the distributed algorithm on a 16 processor transputer system indicate that speed-up is indeed possible in practice: absolute speed-up of 2 to 3 on 8 processors have been consistently achieved on random graphs. But first and foremost the experiments pinpoint problems inherent in a synchronized implementation. Possible improvements are discussed.