Abstract
In this paper we propose two associative parallel algorithms for the edge update of a minimum spanning tree when an edge is deleted or inserted in the underlying graph. These algorithms are represented as the corresponding procedures implemented on a model of associative parallel systems of the SIMD type with vertical data processing (the STAR–machine). We justify correctness of these procedures and evaluate their time complexity.
This work was supported in part by the Russian Foundation for Basic Research under Grant N 03-01-00399
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References
Chin, F., Houck, D.: Algorithms for Updating Minimum Spanning Trees. J. of Computer and System Sciences 16, 333–344 (1978)
Eppstein, D., Galil, Z., Italiano, G.F., Nissenzweig, A.: Sparsification – A Technique for Speeding Up Dynamic Graph Algorithms. J. of the ACM 44(5), 669–696 (1997)
Foster, C.C.: Content Addressable Parallel Processors. Van Nostrand Reinhold Company, New York (1976)
Frederickson, G.: Data Structure for On-line Updating of Minimum Spanning Trees. SIAM J. Comput. 14, 781–798 (1985)
Krikelis, A., Weems, C.C.: Associative Processing and Processors. IEEE Computer Society Press, Los Alamitos (1997)
Nepomniaschaya, A.S.: Language STAR for Associative and Parallel Computation with Vertical Data Processing. In: Mirenkov, N.N. (ed.) Proc. of the Intern. Conf. Parallel Computing Technologies, pp. 258–265. World Scientific, Singapure (1991)
Nepomniaschaya, A.S., Dvoskina, M.A.: A Simple Implementation of Dijkstra’s Shortest Path Algorithm on Associative Parallel Processors. Fundamenta Informaticae 43, 227–243 (2000)
Nepomniaschaya, A.S.: Comparison of Performing the Prim-Dijkstra Algorithm and the Kruskal Algorithm on Associative Parallel Processors. Cybernetics and System Analysis, Kiev, Naukova Dumka (2), 19–27 (2000) (in Russian. English translation by Plenum Press)
Pawagi, S., Kaser, O.: Optimal Parallel Algorithms for Multiple Updates of Minimum Spanning Trees. Algorithmica 9, 357–381 (1993)
Pawagi, S., Ramakrishnan, I.V.: An O(log n) Algorithm for Parallel Update of Minimum Spanning Trees. Inform. Process. Lett. 22, 223–229 (1986)
Potter, J.L.: Associative Computing: A Programming Paradigm for Massively Parallel Computers, Kent State University. Plenum Press, New York (1992)
Spira, P., Pan, A.: On Finding and Updating Spanning Trees and Shortest Paths. SIAM J. Comput. 4, 375–380 (1975)
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Nepomniaschaya, A.S. (2003). Associative Parallel Algorithms for Dynamic Edge Update of Minimum Spanning Trees. In: Malyshkin, V.E. (eds) Parallel Computing Technologies. PaCT 2003. Lecture Notes in Computer Science, vol 2763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45145-7_12
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DOI: https://doi.org/10.1007/978-3-540-45145-7_12
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