Geometric algorithms for private-cache chip multiprocessors
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
| Hi-index | 0.00 |
We present efficient parallel algorithms for some geometric bipartitioning problems. Our algorithms are designed to run in the CREW PRAM model of parallel computation. These bipartition problems are the following. Given a planar point set S (\left| S \right| = n), a measure \mu acting on S and a pair of values f\mu_1 and \mu_2, does there exist a bipartition S = S_1 \cup S_2 such that \mu(S_{1}) \leqslant \mu_i for i = 1,2? We present efficient parallel algorithms for several measures like diameter under L_\infty and L_1 metric; area, perimeter or length of diagonal of the smallest enclosing axes-parallel rectangle and the side length of the smallest enclosing axes-parallel square. All our parallel algorithms run in O(logn) time using O{n) processors in the CREW PRAM. The work done (processor-time product) by our algorithms matches the time complexity of the best known sequential algorithms for most of these problems. As a by product of our algorithms, we can perform report mode orthogonal range queries in optimal O(logn) time using 0(1 + k/logn) processors, where k is the number of points inside the query range. The processor-time product for this range reporting algorithm is optimal.