Scalable parallel algorithm for fast computation of Transitive Closure of Graphs on Shared Memory Architectures

We present a scalable algorithm that computes the transitive closure of a graph on shared memory architectures using the OpenMP API in C++. Two different parallelization strategies have been presented and the performance of the two algorithms has been compared for several data-sets of varying sizes. We demonstrate the scalability of the best parallel implementation up to 176 threads on a shared memory architecture, by producing a graph with more than 3.82 trillion edges. To the best of our knowledge, this is the first implementation that has computed the transitive closure of such a large graph on a shared memory system. Optimization strategies for better cache utilization for large data-sets have been discussed. The important issue of load balancing has been analyzed and its mitigation using the optimal OpenMP scheduling clause has been discussed in detail.