Efficient parallel graph trimming by arc-consistency

Given a large data graph, trimming techniques can reduce the search space by removing vertices without outgoing edges. One application is to speed up parallel decomposition of graphs into strongly connected components (SCC decomposition), which fundamental step for analyzing graphs. We observe that graph essentially kind arc-consistency problem, and AC-3, AC-4, AC-6 are most relevant algorithms trimming. The existing methods require worst-case $$\mathcal O(nm)$$ time O(n)$$ with n m call these AC-3-based as they much like AC-3 algorithm. In this work, we propose AC-4-based AC-6-based methods. That is, has an improved O(n+m)$$ but requires ; compared trimming, same . parallelize be suitable shared-memory multi-core machines. designed minimize synchronization overhead. For algorithms, also prove correctness analyze complexities work-depth model. experiments, compare three over variety real synthetic on machine, where each core corresponds worker. Specifically, maximum number traversed edges per worker using 16 workers, traverses 58.3 36.5 times more than respectively. fewer other methods, meaningful especially implicit particular, practical running time, achieves high speedups portion trimmable vertices.