Parallel algorithms for transitive reduction for weighted graphs

Abstract. We present a generalization of transitive reduction for weighted graphs and give scalable polynomial algorithms for computing it based on the Floyd-Warshall algorithm for finding shortest paths in graphs. We also show how the algorithms can be optimized for memory efficiency and effectively parallelized to improve the run time. As a consequence, the algorithms can be tuned for modern general purpose graphics processors. Our prototype implementations exhibit significant speedups of more than one order of magnitude compared to their sequential counterparts. Transitive reduction for weighted graphs was instigated by problems in reconstruction of genetic networks. The first experiments in that domain show also encouraging results both regarding run time and the quality of the reconstruction