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Optimal parallel algorithms for finding cut vertices and bridges of interval graphs. (English) Zbl 0764.68054
Summary: We present $$O(\log n)$$ time algorithms in the EREW PRAM model, using $$n/\log n$$ processors, to find cut vertices, bridges, and blocks (often called biconnected components) of an interval graph having $$n$$ vertices. It is assumed the interval graph is represented by an interval model, with ends presorted. If the ends are not presorted, our algorithms, preceded by an optimal sort, from an $$O(\log n)$$ time algorithm using $$n$$ processors, which is shown to be optimal. The algorithms rely heavily on the parallel prefix algorithm.

##### MSC:
 68W15 Distributed algorithms 68Q25 Analysis of algorithms and problem complexity 68R10 Graph theory (including graph drawing) in computer science
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##### References:
 [1] Akl, S.G., The design and analysis of parallel algorithms, (1989), Prentice-Hall Englewood Cliffs, NJ · Zbl 0704.68049 [2] Ben-Or, M., Lower bounds for algebraic computation trees, Proc. 15th ACM ann. symp. on theory of computing, 80-86, (1983) [3] Bertossi, A.A.; Bonuccelli, M.A., Some parallel algorithms on interval graphs, Discrete appl. math., 16, 101-111, (1987) · Zbl 0636.68087 [4] Bollobos, B., Graph theory, (1979), Springer New York [5] Cole, R., Parallel merge sort, SIAM J. comput., 17, 770-785, (1988) · Zbl 0651.68077 [6] Dekel, E.; Sahni, S., Binary trees and parallel scheduling algorithms, IEEE trans. comput., 32, 307-315, (1983) · Zbl 0513.68031 [7] Golumbic, M.C., Algorithmic graph theory and perfect graphs, (1980), Academic Press New York · Zbl 0541.05054 [8] Harary, F., Graph theory, (1969), Addison-Wesley Reading, MA · Zbl 0797.05064 [9] Kim, S.K., Optimal parallel algorithms on sorted intervals, Proc. 27th ann. allerton conf. on comm., control, and computing, 766-775, (1989) [10] Kruskal, C.P.; Rudolph, L.; Snir, M., The power of parallel prefix, IEEE trans. comput., 34, 965-968, (1985) [11] Olariu, S.; Schwing, J.L.; Zhang, J., Optimal parallel algorithms for problems modelled by a family of intervals, Proc. 28th ann. allerton conf. on comm., control, and computing, 282-291, (1990) [12] Preparata, F.P.; Shamos, M.I., Computational geometry: an introduction, (1988), Springer New York [13] Ramkumar, G.D.S.; Pandu Rangan, C., Parallel algorithms on interval graphs, Proc. 1990 internat. conf. on parallel processing, Vol. 3, 72-74, (1990) [14] Tarjan, R.E.; Vishkin, U., An efficient parallel biconnectivity algorithm, SIAM J. comput., 14, 862-874, (1985) · Zbl 0575.68066 [15] Tsin, Y.H.; Chin, F.Y., Efficient parallel algorithms for a class of graph theoretic problems, SIAM J. comput., 13, 580-599, (1984) · Zbl 0545.68060 [16] Yoshimura, T.; Kuh, E.S., Efficient algorithms for channel routing, IEEE trans. comput. aided design, 1, 25-35, (1982)
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