N. M. Amato and E. A. Ramos. On computing Voronoi diagrams by divideprune -and-conquer. In Proc. 12th Annu. ACM Sympos. Comput. Geom., pages 166--175, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Overmars. Key words. computational geometry, convex polytopes, lower bounds, decision trees, adversary arguments AMS subject classifications. 68Q25, 68U05, 52B55, 52B05 1. Introduction. The construction of convex hulls is one of the most basic and well studied problems in computational geometry [2,3,5,10,11,12,13,15,17,18, 29,34,35,38,39,47,41,45,43,44,47,48]. Over twentyyears ago, Graham described an algorithm that constructs the convex hull of n points in the plane in O(n log n) time [29] The same running time was first achieved in three dimensions by Preparata and Hong [38] Yao [48] proved a lower bound of Omega n log n) on the complexity of ....

.... hulls in arbitrary dimensions in time O(nf )# see also [47] Seidel s shelling algorithm runs in time O(n 2 f log n) 43] A divide and conquer algorithm of Chan, Snoeyink, and Yap [12] constructs four dimensional hulls in time O( n f)log 2 f ) and a recent improvementby Amato and Ramos [2] constructs five dimensional hulls in time This researchwas done while the author was a graduate studentatU.C.Berkeley,withthe support of a Graduate Assistance in Areas of National Need Fellowship. An extended abstract of this paper was presented at the 12th Annual ACM Symposium on Computational ....

[Article contains additional citation context not shown here]

N. M. Amato and E. A. Ramos, On computing Voronoi diagrams by divide-prune-andconquer, in Proc. 12th Annu. ACM Sympos. Comput. Geom., 1996, pp. 166--175.

....f log(n) for facet enumeration and O(n 2 L log(n) for computing the facial lattice. There are a couple of divide and conquer algorithms that construct the convex hull in: ffl 4 dimensions in O( n f) log 2 f) time and O(n f) space ( 9] ffl 5 dimensions in O( n f) log 3 f) time ([1]) Erickson showed that, in the worst case, Omega Gamma n dd=2e Gamma1 n log n) time is needed to determine the number of convex hull facets ( 5] For odd dimensions, this matches Chazelle s upper bound. 12 7 Two dimensions revisited This section discusses output sensitive algorithms for ....

N.M. Amato and E.A. Ramos. On computing Voronoi diagrams by divide-prune-and-conquer. Proceedings of the 12th Annual ACM Symposium on Computational Geometry, pages 166-175, 1996.

....geometry, convex polytopes, degeneracy, lower bounds, decision trees, adversary arguments AMS subject classifications. 68Q25, 68U05, 52B55, 52B05 PII. S0097539797315410 1. Introduction. The construction of convex hulls is one of the most basic and well studied problems in computational geometry [2, 3, 5, 10, 11, 12, 13, 15, 17, 18, 29, 34, 35, 38, 39, 47, 41, 45, 43, 44, 48]. Over 20 years ago, Graham described an algorithm that constructs the convex hull of n points in the plane in O(n log n) time [29] The same running time was first achieved in three dimensions by Preparata and Hong [38] Yao [48] proved a lower bound of ## n log n) on the complexity of ....

.... 1199 bitrary dimensions in time O(nf ) see also [47] Seidel s shelling algorithm runs in time O(n 2 f log n) 43] A divide and conquer algorithm of Chan, Snoeyink, and Yap [12] constructs four dimensional hulls in time O( n f) log 2 f ) and a recent improvement by Amato and Ramos [2] constructs five dimensional hulls in time O( n f) log 3 f ) In dimensions higher than five, the fastest algorithms are an improvement of the gift wrapping algorithm by Chan [11] with running time O(n log f (nf) 1 1 (#d 2# 1) polylog n) an extension of Chan, Snoeyink, and Yap s ....

[Article contains additional citation context not shown here]

<F4.683e+05> N. M. Amato and E. A.<F3.852e+05> Ramos,<F3.712e+05> On computing Voronoi diagrams by divide-prune-andconquer,<F3.852e+05> in Proceedings of the 12th ACM Sympos. Comput. Geom., Philadelphia, PA, 1996, pp. 166--175.

....are in harmony with me and sustain me. 22. Laugh away these facts and truths if you can. Carl Theodore Heisel, The Circle Squared Beyond Refutation, 31 Chapter 3 Convex Hull Problems The construction of convex hulls is perhaps the oldest and best studied problems in computational geometry [6, 10, 11, 12, 29, 28, 30, 36, 49, 50, 91, 101, 110, 123, 130, 132, 134, 136, 142]. Over twenty years ago, Graham described an algorithm that constructs the convex hull of n points in the plane in O(n log n) time [91] The same running time was first achieved in three dimensions by Preparata and Hong [123] Yao [154] proved a lower bound of Omega (n log n) on the complexity of ....

....1970, Chand and Kapur [30] described an algorithm that constructs convex hulls in time O(nf) where f is the number of facets in the output. An algorithm of Chan, Snoeyink, and Yap [28] constructs four dimensional hulls in time O( n f) log 2 f) and 32 a recent improvement by Amato and Ramos [6] constructs five dimensional hulls in time O( n f) log 3 f) The fastest algorithm in higher dimensions, due to Chan [29] runs in time O(n log f (nf) 1 1= bd=2c 1) polylog n) this algorithm is optimal when f is sufficiently small. For related results, see [10, 30, 49, 50, 101, 134] ....

[Article contains additional citation context not shown here]

Nancy M. Amato and Edgar A. Ramos. On computing Voronoi diagrams by divideprune -and-conquer. In Proc. 12th Annu. ACM Sympos. Comput. Geom., pages 166--175, 1996.

....that is left open is then to find a convex hull algorithm in E d (d 4) with close to O(n log f f) running time for the whole range of output size f . Improving our O( n f) log 2 f) bound in E 4 would also be interesting. Note: After the submission of this paper, Amato and Ramos [2] have recently announced an extension of our 4 d algorithm to 5 d, running in O( n f) log 3 f) time. They also describe how to adapt our 4 d algorithm to work with degenerate point sets. Acknowledgements We thank Nancy Amato, Otfried Schwarzkopf, John Hershberger, and Subhash Suri for ....

N. M. Amato and E. A. Ramos. On computing Voronoi diagrams by divide-prune-and-conquer. In Proceedings of the 12th Annual ACM Symposium on Computational Geometry, pages 166--175, 1996.

....Overmars. Key words. computational geometry, convex polytopes, lower bounds, decision trees, adversary arguments AMS subject classifications. 68Q25, 68U05, 52B55, 52B05 1. Introduction. The construction of convex hulls is one of the most basic and well studied problems in computational geometry [2, 3, 5, 10, 11, 12, 13, 15, 17, 18, 29, 34, 35, 38, 39, 47, 41, 45, 43, 44, 47, 48]. Over twenty years ago, Graham described an algorithm that constructs the convex hull of n points in the plane in O(n log n) time [29] The same running time was first achieved in three dimensions by Preparata and Hong [38] Yao [48] proved a lower bound of Omega Gamma n log n) on the ....

.... in arbitrary dimensions in time O(nf ) see also [47] Seidel s shelling algorithm runs in time O(n 2 f log n) 43] A divide and conquer algorithm of Chan, Snoeyink, and Yap [12] constructs four dimensional hulls in time O( n f) log 2 f ) and a recent improvement by Amato and Ramos [2] constructs five dimensional hulls in time This research was done while the author was a graduate student at U. C. Berkeley, with the support of a Graduate Assistance in Areas of National Need Fellowship. An extended abstract of this paper was presented at the 12th Annual ACM Symposium on ....

[Article contains additional citation context not shown here]

N. M. Amato and E. A. Ramos, On computing Voronoi diagrams by divide-prune-andconquer, in Proc. 12th Annu. ACM Sympos. Comput. Geom., 1996, pp. 166--175.

.... in contrast to O(log 2 n) for the rst algorithm in this paper and the previous one [8] The approach of divide and conquer with partial clean up also simpli es other previous algorithms (3 d convex hulls, 2 d abstract Voronoi diagrams, 3 d diameter, single face in an arrangement of segments [7, 8, 10]) and also leads to the same time speed up for the corresponding parallel algorithms of some of them (3 d convex hulls, 2 d abstract Voronoi diagrams) We present here the algorithm for computing a single face in an arrangement of curve segments and leave the other applications for a ....

.... algorithm in this paper, and to the previous algorithm in [8] which have a running time O(log 2 n) The approach of divide and conquer with partial clean up also simpli es other algorithms (3 d convex hulls, 2 d abstract Voronoi diagrams, 3 d diameter, single face in an arrangement of segments [7, 8, 10]) and also leads to the same time speed up for the corresponding parallel algorithms (3 d convex hulls, 2 d abstract Voronoi diagrams) We present here the algorithm for the single face problem and leave the other results for a companion paper [9] Finally, we discuss implementations in the CRCW ....

N. M. Amato and E. A. Ramos. On computing Voronoi diagrams by divide-prune-and-conquer. In Proc. 12th Annual ACM Sympos. Comput. Geom., 166-175, 1996.

....on random sampling. The approach extends previous work by Dehne et al. 7] Deng and Zhu [8] and Kuhn [9] that use small separators for planar graphs in the design of randomized geometric algorithms for coarse grained multicomputers. The approach simplifies other previous geometric algorithms [1, 2], and also has the potential of providing efficient deterministic algorithms for the external memory model. 1 Problem and Previous Work We consider a classical problem in computational geometry: computing the arrangement determined by a set of curve segments in the plane. There has been a ....

....deterministic algorithm for computing a (1=r) cutting of optimal size for an arrangement of segments. The divide and conquer with partial clean up approach also simplifies other algorithms (3 d convex hulls, 2 d abstract Voronoi diagrams, 3 d diameter, single face in an arrangement of segments [1, 2]) and leads to the same time speed up for the corresponding parallel algorithms. These results will appear in a companion paper. We expect that the approach will find further applications. Specifically, in the design of deterministic geometric algorithms in the external memory model. A complete ....

N. M. Amato and E. A. Ramos. On computing Voronoi diagrams by divide-prune-and-conquer. In Proc. 12th Annual ACM Sympos. Comput. Geom., 672--682, 1996.

.... algorithm in this paper, and to the previous algorithm in [8] which have a running time O(log 2 n) The approach of divide and conquer with partial clean up also simpli es other algorithms (3 d convex hulls, 2 d abstract Voronoi diagrams, 3 d diameter, single face in an arrangement of segments [7, 8, 10]) and also leads to the same time speed up for the corresponding parallel algorithms (3 d convex hulls, 2 d abstract Voronoi diagrams) These results are reported in a companion paper [9] We expect that the approach will nd further applications. We also present an algorithm for computing a ....

N. M. Amato and E. A. Ramos. On computing Voronoi diagrams by divide-prune-and-conquer. In Proc. 12th Annual ACM Sympos. Comput. Geom., 166-175, 1996.

No context found.

N. M. Amato and E. A. Ramos. On computing Voronoi diagrams by divideprune -and-conquer. In Proc. 12th Annu. ACM Sympos. Comput. Geom., pages 166--175, 1996.

No context found.

Nancy M. Amato and Edgar A. Ramos. On computing Voronoi diagrams by divideprune -and-conquer. In Proc. 12th Annu. ACM Sympos. Comput. Geom., pages 166--175, 1996.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC