The strongly connected components of a directed graph can be found in an optimal linear time, by algorithms based on depth first search. Unfortunately, depth first search is difficult to parallelize. We describe two divide-and-conquer algorithms for this problem that have significantly greater potential for parallelization. We show the expected serial runtime of our simpler algorithm to be O(m log n), for a graph with n vertices and m edges.We then show that the second algorithm has O(m log n) worst–case complexity.
By: Don Coppersmith; Lisa Fleischer; Bruce Hendrickson; Ali Pinar
Published in: RC23744 in 2005
LIMITED DISTRIBUTION NOTICE:
This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.
Questions about this service can be mailed to reports@us.ibm.com .