Abstract
In this paper, we consider parallel algorithms for shortest pa- ths and related problems on trapezoid graphs under the CREW PRAM model. Given a trapezoid graph with its corresponding trapezoid dia- gram, we present parallel algorithms solving the following problems: For the single-source shortest path problem, the algorithm runs in O(log n) time using O(n) processors and space. For the all-pair shortest path query problem, after spending O(log n) preprocessing time using O(n log n) space and O(n) processors, the algorithm can answer the query in O(log δ) time using one processor. Here δ denotes the distance between two queried vertices. For the minimum cardinality Steiner set problem, the algorithm runs in O(log n) time using O(n) processors and space.
We also extend our results to the generalized trapezoid graphs. The single-source shortest path problem and the minimum cardinality Steiner set problem on d-trapezoid graphs and circular d-trapezoid graphs can both be solved in O(log n log d) time using O(nd) space and O(d 2 n/log d) processors. The all-pair shortest path query problem on d-trapezoid graphs and circular d-trapezoid graphs can be answered in O(d log δ) time using one processor after spending O(log n log d) preprocessing time using O(nd log n) space and O(d 2 n/log d) processors.
Support in part by the National Science Council, Taiwan, R.O.C, grant NSC-89-213-E-126-007.
Corresponding author, Department of Accounting.
The corresponding address for the second and the third authors is Department of Computer Science and Information Management.
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© 1999 Springer-Verlag Berlin Heidelberg
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Hsu, F.R., Lin, YL., Tsai, YT. (1999). Parallel Algorithms for Shortest Paths and Related Problems on Trapezoid Graphs. In: Algorithms and Computation. ISAAC 1999. Lecture Notes in Computer Science, vol 1741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46632-0_18
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DOI: https://doi.org/10.1007/3-540-46632-0_18
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