A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
The complexity of parallel search
Journal of Computer and System Sciences - 17th Annual ACM Symposium in the Theory of Computing, May 6-8, 1985
A new parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
Transitive compaction in parallel via branchings
Journal of Algorithms
On finding minimal 2-connected subgraphs
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The Complexity of Finding Minimal Spanning Subgraphs
The Complexity of Finding Minimal Spanning Subgraphs
Biconnectivity approximations and graph carvings
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Biconnectivity approximations and graph carvings
Journal of the ACM (JACM)
Approximating unweighted connectivity problems in parallel
Information and Computation
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Let P be a property of undirected graphs. We consider the following problem: given a graph G that has property P, find a minimal spanning subgraph of G with property P. We describe two related algorithms for this problem and prove their correctness under some rather weak assumptions about P. We devise a general technique for analyzing the worst-case behavior of these algorithms. By applying the technique to 2-edge-connectivity and biconnectivity, we obtain an &OHgr;(m + n log n) lower bound on the worst-case running time of the algorithms for these two properties, thus settling open questions posed earlier with regard to these properties. We then describe refinements of the basic algorithms that yield the first linear-time algorithms for finding a minimal 2-edge-connected spanning subgraph and a minimal biconnected spanning subgraph of a graph.