An efficient method is presented for finding blocks and cutnodes of an arbitrary undirected graph. The graph may be represented either (i) as an ordered list of edges or (ii) as a packed adjacency matrix. If w denotes the word length of the machine employed, the storage (in machine words) required for a graph with n nodes and m edges increases essentially as 2(m + n) in case (i), or n2/w in case (ii). A spanning tree with labeled edges is grown, two edges finally bearing different labels if and only if they belong to different blocks. For both representations the time required to analyze a graph on n nodes increases as n&ggr; where &ggr; depends on the type of graph, 1 ≤ &ggr; ≤ 2, and both bounds are attained. Values of &ggr; are derived for each of several suitable families of test graphs, generated by an extension of the web grammar approach. The algorithm is compared in detail with that proposed by Read for which 1 ≤ &ggr; ≤ 3.
The Latest from CACM
Shape the Future of Computing
ACM encourages its members to take a direct hand in shaping the future of the association. There are more ways than ever to get involved.
Get InvolvedCommunications of the ACM (CACM) is now a fully Open Access publication.
By opening CACM to the world, we hope to increase engagement among the broader computer science community and encourage non-members to discover the rich resources ACM has to offer.
Learn More
Join the Discussion (0)
Become a Member or Sign In to Post a Comment