Multi-core on-the-fly SCC decomposition

Abstract

The main advantages of Tarjan's strongly connected component (SCC) algorithm are its linear time complexity and ability to return SCCs on-the-fly, while traversing or even generating the graph. Until now, most parallel SCC algorithms sacrifice both: they run in quadratic worst-case time and/or require the full graph in advance. The current paper presents a novel parallel, on-the-fly SCC algorithm. It preserves the linear-time property by letting workers explore the graph randomly while carefully communicating partially completed SCCs. We prove that this strategy is correct. For efficiently communicating partial SCCs, we develop a concurrent, iterable disjoint set structure (combining the union-find data structure with a cyclic list). We demonstrate scalability on a 64-core machine using 75 real-world graphs (from model checking and explicit data graphs), synthetic graphs (combinations of trees, cycles and linear graphs), and random graphs. Previous work did not show speedups for graphs containing a large SCC. We observe that our parallel algorithm is typically 10-30× faster compared to Tarjan's algorithm for graphs containing a large SCC. Comparable performance (with respect to the current state-of-the-art) is obtained for graphs containing many small SCCs.

Combining Parallel Emptiness Checks with Partial Order Reductions

“…We fix the maximum running time to 40 minutes. 3 Here we compute only a reduced LTS explored by the algorithms presented in the previous sections. When applied in the context of a model checker, the visited reduced LTS will be larger due to the observation of visible transitions [23].…”

“…According to Bloemen et al [3], the performances of parallel emptiness checks may rely on the underlying graph structure. To evaluate this, the 21 models selected are divided into two categories: M 1 (models with short cycles and many small SCCs) and M 2 (models with long cycles and a small number of large SCCs).…”

“…To evaluate this, the 21 models selected are divided into two categories: M 1 (models with short cycles and many small SCCs) and M 2 (models with long cycles and a small number of large SCCs). Bloemen et al [3] observe that the performances for the algorithm suggested by Renault et al [24] are degraded for M 2 which is the motivation of the introduction of their new algorithm.…”

Short Paper: Maintenance of Strongly Connected Component in Shared-Memory Graph

“…We always maintain a invariant that any unmarkable node is always reachable from the respective Head of the list. In the Fig 2, we have shown an example after addition of the edge (8,3) in the Fig 1(a), how all three SCCs are merged to form a new SCC. A new vertex newv is added by invoking AddVertex method.…”

“…For any u, v ∈ C: u and v are strongly connected. 3. For any u ∈ C and v ∈ V − C: u and v are not strongly connected.…”