Abstract
Few existing parallel graph algorithms achieve optimality when applied to very sparse graphs such as planar graphs. We add to the list of such algorithms by giving optimal, logarithmic-time PRAM algorithms for the connected components, spanning tree, biconnected components, and strong orientation problems. The algorithms work on classes of graphs including planar graphs and graphs of bounded genus or bounded thickness.
Supported by the DFG, SFB 124, TP B2, VLSI Entwurfsmethoden und Parallelität.
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Francis Y. Chin, John Lam, and I-Ngo Chen: “Efficient Parallel Algorithms for Some Graph Problems”. Communications of the ACM 25 (1982), 659–665.
Richard Cole and Uzi Vishkin: “Approximate and exact parallel scheduling with applications to list, tree and graph problems”. Proceedings, 27th Annual Symposium on Foundations of Computer Science (1986), 478–491.
Richard Cole and Uzi Vishkin: “Faster Optimal Parallel Prefix Sums and List Ranking”. To appear in Information and Computation.
Richard Cole and Uzi Vishkin: “Approximate parallel scheduling. Part II: Applications to optimal parallel graph algorithms in logarithmic time”. Preprint, 1987.
Faith E. Fich, Prabhakar L. Ragde and Avi Wigderson: “Relations Between Concurrent-Write Models of Parallel Computation”. Proceedings, 3rd Annual ACM Symposium on Principles of Distributed Computing (1984), 179–189.
Hillel Gazit: “An Optimal Randomized Parallel Algorithm for Finding Connected Components in a Graph”. Proceedings, 27th Annual Symposium on Foundations of Computer Science (1986), 492–501.
Alan Gibbons and Wojciech Rytter: “Optimal Parallel Algorithms for Dynamic Expression Evaluation and Context-Free Recognition”. Preprint, 1987.
Torben Hagerup: “Towards Optimal Parallel Bucket Sorting”. Information and Computation 75 (1987), 39–51.
Torben Hagerup: “A Note on Saving Space in Parallel Computation”. Submitted to Information Processing Letters.
Frank Harary: “Graph Theory”. Addison-Wesley, Reading, Mass., 1969.
D. S. Hirschberg, A. K. Chandra and D. V. Sarwate: “Computing Connected Components on Parallel Computers”. Communications of the ACM 22 (1979), 461–464.
Gary L. Miller and John H. Reif: “Parallel Tree Contraction and Its Application”. Proceedings, 26th Annual Symposium on Foundations of Computer Science (1985), 478–489.
Yossi Shiloach and Uzi Vishkin: “An O(log n) Parallel Connectivity Algorithm”. Journal of Algorithms 3 (1982), 57–67.
Robert E. Tarjan and Uzi Vishkin: “An Efficient Parallel Biconnectivity Algorithm”. SIAM Journal on Computation 14 (1985), 862–874.
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© 1988 Springer-Verlag Berlin Heidelberg
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Hagerup, T. (1988). Optimal parallel algorithms on planar graphs. In: Reif, J.H. (eds) VLSI Algorithms and Architectures. AWOC 1988. Lecture Notes in Computer Science, vol 319. Springer, New York, NY. https://doi.org/10.1007/BFb0040370
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DOI: https://doi.org/10.1007/BFb0040370
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Print ISBN: 978-0-387-96818-6
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