Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
On the general motion-planning problem with two degrees of freedom
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Scalable parallel geometric algorithms for coarse grained multicomputers
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Parallel computing (2nd ed.): theory and practice
Parallel computing (2nd ed.): theory and practice
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Optimal, output-sensitive algorithms for constructing planar hulls in parallel
Computational Geometry: Theory and Applications
Theoretical Computer Science
The Parallel Evaluation of General Arithmetic Expressions
Journal of the ACM (JACM)
On Computing the Upper Envelope of Segments in Parallel
ICPP '98 Proceedings of the 1998 International Conference on Parallel Processing
Waste makes haste: tight bounds for loose parallel sorting
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
| Hi-index | 0.00 |
The importance of the sensitivity of an algorithm to the output size of a problem is well-known especially if the upper bound on the output size is known to be not too large. In this paper we focus on the problem of designing very fast parallel algorithms for constructing the upper envelope of straight-line segments that achieve the O(nlogH) work-bound for input size n and output size H. When the output size is small, our algorithms run faster than the algorithms whose running times are sensitive only to the input size. Since the upper bound on the output size of the upper envelop problem is known to be small (n@a(n)), where @a(n) is a slowly growing inverse-Ackerman's function, the algorithms are no worse in cost than the previous algorithms in the worst case of the output size. Our algorithms are designed for the arbitrary CRCW PRAM model. We first describe an O(logn.(logH+loglogn)) time deterministic algorithm for the problem, that achieves O(nlogH) work bound for H=@W(logn). We then present a fast randomized algorithm that runs in expected time O(logH.loglogn) with high probability and does O(nlogH) work. For logH=@W(loglogn), we can achieve the running time of O(logH) while simultaneously keeping the work optimal. We also present a fast randomized algorithm that runs in O@?(logn/logk) time with nk processors, klog^@W^(^1^)n. The algorithms do not assume any prior input distribution and the running times hold with high probability.