Optimizing the Critical Path of Distributed Dataflow Graph Algorithms

Executing graph algorithms in a parallel or distributed context is a challenging problem. Solving race conditions with locks is usually prohibitively expensive and some algorithms opt for a strategy that ignores the race condition altogether and corrects later the derived solution if it is invalid. Alternatively, dataflow algorithms solve the synchronization problem by executing the algorithm by following a partial order on the graph. While removing the cost of locks or avoiding a checking phase improves performance, it is possible that the algorithm picks a partial order with long chains, which limit parallelism. In this paper, we investigate how distributed dataflow graph algorithm obtain a partial order and how one could favor orders with shorter long chains. Most dataflow algorithms obtain their order by having each vertex of the graph pick a uniformly random number in [0; 1) and order the vertices based on that number. We believe that this type of order could lead to long chains in graphs with dense regions such as small world graph. We design two alternative ways of generating the order to make it similar to a largest degree first order. We study the behavior of these different algorithms on a wide range of randomly generated RMAT graphs and on a set of real world graphs. And we show that our ordering methods can significantly reduce the length of the longest chain.