Fast parallel algorithms for finding elementary circuits of a directed graph: a GPU-based approach

Abstract

Circuits in a graph are interesting structures and identifying them is of an important relevance for many applications. However, enumerating circuits is known to be a difficult problem, since their number can grow exponentially. In this paper, we propose fast parallel approaches for enumerating elementary circuits of a directed graphs based on Graphics Processing Unit (GPU). Our algorithms are based on a massive exploration of the graph in a Breadth First Search (BFS) strategy. Algorithm V-FEC explores the graph starting from different vertices simultaneously. To further reduce the search space, we present T-FEC, another algorithm that uses triplets as an initial set to start exploring. To the best of our knowledge, those are the first parallel GPU-based algorithms for finding all circuits of a given graph. The evaluation results show that the proposed approaches achieves up to 190x speed-up over Johnson's algorithm, one of the most efficient sequential algorithms for finding circuits.