Distributed Algorithms for Cyclic Edge Connectivity and Cyclic Vertex Connectivity of Cubic Graphs
Jun Liang, Meixin Du, Ruihua Nie, Zhihao Liang, Zheng Li · 2020
For a connected graph G, a set S of edges (vertices) is a cyclic edge (vertex) cutset if G - S is not connected and at least two components contain a cycle respectively. The cyclic edge (vertex) connectivity cλ (κ) is the cardinality of a minimum cyclic edge (vertex) cutset. In this paper, we gave distributed algorithms determining cyclic edge connectivity and cyclic vertex connectivity of cubic graphs. The experiment results showed that the distributed algorithms were significantly improved in time compared to the original algorithms when the graph was large. Time costs of the distributed algorithms separately for cyclic edge connectivity and cyclic vertex connectivity are correspondingly less than 33% and less than 40% that of the single machine algorithms when the graph was large enough.