An efficient incremental strongly connected components algorithm for evolving directed graphs

Abstract

The strongly connected components (SCC) algorithm can contract a directed graph into a directed acyclic graph and is widely used in directed graph analysis applications, such as reachability queries. A variety of SCC algorithms for static directed graphs have been proposed but such algorithms require non-negligible runtime overheads to repeatedly perform computations on an entire graph in response to the frequent changes in the evolving directed graphs that are ubiquitous in the real world. In general, evolving directed graphs are often evolving with minor changes (less than 5%).It allows us to compute SCC in an evolving directed graph on the basis of incremental computations in order to reduce the response time. This paper proposes Inc-SCC, an efficient incremental SCC algorithm for evolving directed graphs, reducing the data access and computation overhead of the algorithm by eliminating unnecessary computations, and using the disjoint feature of SCC for parallel processing to improve the performance of the SCC algorithm. We propose a heuristic optimization method to further speed up the convergence of Inc-SCC. Experiments show that Inc-SCC can be used to enhance the timeliness for evolving directed graphs. When the number of the changed edges of the entire directed graph is 5%, the speedup of Inc-SCC over the existing algorithm is from 2.8 to 12 times. When the number of thechanged edges of an entire directed graph is 0.5%, the speedup of Inc-SCC over the existing algorithm is from 2.9 to 12 times.