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Efficient parallel algorithms for the r-dominating set and p-center problems on trees

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2 Author(s)
Tzu-Chin Lin ; Dept. of Comput. Sci., Nat. Tsing Hua Univ., Hsinchu, Taiwan ; Biing-Feng Wang

Let T=(V, E) be a tree with vertex set V and edge set E. Let n=|V|. Each e∈E has a non-negative length. In this paper, we first present an algorithm on the CREW PRAM for solving the V/V/r-dominating set problem on T, where r≥0 is a real number. The algorithm requires O(log2 n) time using O(n log n) work. Applying this algorithm as a procedure for testing feasibility, the V/V/p-center problem on the CREW PRAM is solved in O(log2 n) time using O(n log2 n) work, where p≥1 is an integer. Previously, He and Yesha had proposed algorithms on the CREW PRAM for special cases of the V/V/r-dominating set and the V/V/p-center problems, in which r is an integer and the lengths of all edges are 1. Their V/V/r-dominating set algorithm requires O(log n log log n) time using O(n log n log log n) work; and their V/V/p-center algorithm requires O(log2 n log log n) time using O(n log2 n log log n) work. As compared with He and Yesha's results, ours are more general and more efficient from the aspect of work.

Published in:

Parallel and Distributed Systems, 2002. Proceedings. Ninth International Conference on

Date of Conference:

17-20 Dec. 2002