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Solving NP-hard problems in ’almost trees’: vertex cover. (English) Zbl 0573.68017
In the paper a new algorithm which finds a minimum vertex cover in a graph G, is proposed. Its complexity depends linearly on the number of vertices of G and exponentially on the maximum a over all biconnected components of the graph, where a is defined as the minimum number of edges that must be added to a tree to produce G. A parallel implementation of the algorithm is also given.
Reviewer: J.Bła.zewicz

68Q25Analysis of algorithms and problem complexity
68R10Graph theory in connection with computer science (including graph drawing)
Full Text: DOI
[1] Garey, M. R.; Johnson, D. S.: Computers and intractability -- A guide to the theory of NP-completeness. (1979) · Zbl 0411.68039
[2] Gurevich, Y.; Stockmeyer, L.; Vishkin, U.: Solving NP-hard problems on graphs that are almost trees and an application to facility location problems. J. ACM 31, 459-473 (1984) · Zbl 0629.68042
[3] Megiddo, N.: Applying parallel computation in the design of serial algorithms. J. ACM 30, 852-865 (1983) · Zbl 0627.68034
[4] Tarjan, R. E.: Depth first search and linear graph algorithms. SIAM J. Comput. 1, 146-160 (1972) · Zbl 0251.05107
[5] Tarjan, R. E.; Trojanowski, A. E.: Finding a maximum independent set. SIAM J. Comput. 6, 537-546 (1977) · Zbl 0357.68035
[6] R.E. Tarjan and U. Vishkin, An efficient parallel biconnectivity algorithm, TR-69, Dept. of Comp. Sci., Courant Inst., New York Univ., 251 Mercer St., NY 10012, to appear in SIAM J. Comput. · Zbl 0575.68066
[7] U. Vishkin, Synchronous parallel computation -- a survey, TR-71, Dept. of Comp. Sci., Courant Inst., New York Univ., 251 Mercer St., NY 10012.