Abstract
In this paper is presented a parallel algorithm to find a maximal matching on a minimal vertex series parallel dag. The algorithm requires O(m) processors and runs in O(logn) parallel time on a PRAM-EREW model of computation. This algorithm improves of a factor log n the parallel time of the general algorithm when it is specified to this class of graphs. Also the number of processors decreases from O(n + m) to O(m).
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References
S. Baase, Introduction to parallel connectivity, list ranking and Euler tour tecniques, (see [15]), (1993), pp. 61–114.
C. Berge, Graphs and Hypergraphs, North-Holland (1970).
G.E. Blelloch, Prefix sums and their applications, (see [15]), (1993), pp. 35–60.
R. Cole, Parallel merge sort, (see [15]), (1993), pp. 453–494.
A. K. Datta, R. K. Sen, An efficient Parallel Algorithm for Maximal Matching, INCS 634, (1993), pp. 813–814.
R. J. Duffin, Topology of series-parallel networks, J. Mathematical Analysis and Applications 10, (1965), pp. 303–318.
Gimbel, J.W.Kennedy and L.V. Quintas, Quo vadis, graph theory?, Elsevier Science Publishers, N.Y. (1993).
F. Harary and R. Norman, Some properties of line-digraphs, Rendiconti del Circolo Matematico Palermo, Vol 9, 1960, pp. 149–163.
X. He and Y. Yesha, Binary tree algebraic computation and parallel algorithms for simple graphs, Journal of Agorithms, Vol 9, 1988, pp. 92–113.
E. L. Lawler, Sequencing jobs to minimize total weighted completion time subject to precedence constraints, Annals of Discrete Math., Vol 2, (1978), pp. 75–90.
M. Luby, Removing randomness in parallel computation without a processor penalty, Journal of Computer and System Sciences, Vol 47(2), (1993), pp. 250–286.
C. L. Monma, and J.B. Sidney, A general algorithm for optimal job sequencing with series-parallel constraints, Math. of Operations Research, Vol 4, (1977), 215–224.
C.H. Papadimitrou and K. Steiglitz, Combinatorial optimization: algorithm and complexity, Prentice Hall, Inc. Englewood Cliffs, New Jersey 1982.
M.D.Plummer, Matching and vertex packing: how ”hard” are they?, (see [7]), (1993), pp. 275–312.
J. H. Reif, Synthesis of parallel algorithms, Morgan Kaufmann Publishers, San Mateo, California (1993).
J. Valdes, R.E. Tarjan and E.L. Lawler, The recognition of series parallel digraphs, SIAM Journal of Computation, Vol 11, no 2, 1982, pp.298–313.
J. Van Leeuwen, Handbook of Theorical Computer Science, Vol A: Algorithms and Complexity, Elsevier Science Publishers, Amsterdam (1990).
J. Van Leeuwen, Graph algorithms, (see [17]), (1990), pp. 527–631.
V.V. Vazirani, Parallel graph matching, (see [15]), (1993), pp. 783–811.
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© 1995 Springer-Verlag Berlin Heidelberg
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Baffi, L., Petreschi, R. (1995). Parallel maximal matching on minimal vertex series parallel digraphs. In: Kanchanasut, K., Lévy, JJ. (eds) Algorithms, Concurrency and Knowledge. ACSC 1995. Lecture Notes in Computer Science, vol 1023. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60688-2_33
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DOI: https://doi.org/10.1007/3-540-60688-2_33
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