Computational geometry: an introduction
Computational geometry: an introduction
Planar point location using persistent search trees
Communications of the ACM
An implicit data structure supporting insertion, deletion, and search in O(log:OS2:OEn) time
Journal of Computer and System Sciences
Optimal point location in a monotone subdivision
SIAM Journal on Computing
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
An optimal algorithm for intersecting line segments in the plane
Journal of the ACM (JACM)
An optimal algorithm for finding segments intersections
Proceedings of the eleventh annual symposium on Computational geometry
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
On the exact worst case query complexity of planar point location
Journal of Algorithms
Incremental constructions con BRIO
Proceedings of the nineteenth annual symposium on Computational geometry
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Towards in-place geometric algorithms and data structures
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Space-efficient planar convex hull algorithms
Theoretical Computer Science - Latin American theorotical informatics
Implicit B-trees: a new data structure for the dictionary problem
Journal of Computer and System Sciences - Special issue on FOCS 2002
An in-place sorting with O(nlog n) comparisons and O(n) moves
Journal of the ACM (JACM)
Optimal Implicit Dictionaries over Unbounded Universes
Theory of Computing Systems
Space-efficient algorithms for computing the convex hull of a simple polygonal line in linear time
Computational Geometry: Theory and Applications
Planar Point Location in Sublogarithmic Time
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Space-efficient geometric divide-and-conquer algorithms
Computational Geometry: Theory and Applications
Line-segment intersection made in-place
Computational Geometry: Theory and Applications
In-place 2-d nearest neighbor search
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Succinct geometric indexes supporting point location queries
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Radix sorting with no extra space
ESA'07 Proceedings of the 15th annual European conference on Algorithms
In-Place algorithms for computing (layers of) maxima
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
I/O-efficient construction of constrained delaunay triangulations
ESA'05 Proceedings of the 13th annual European conference on Algorithms
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
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We describe the first optimal randomized in-place algorithm for the basic 3-d convex hull problem (and, in particular, for 2-d Voronoi diagrams). The algorithm runs in O(n log n) expected time using only O(1) extra space; this improves the previous O(n log3 n) bound by Bronnimann, Chan, and Chen [SoCG'04]. The same approach leads to an optimal randomized in-place algorithm for the 2-d line segment intersection problem, with O(n log n+K) expected running time for output size K, improving the previous O(n log2 n + K) bound by Vahrenhold [WADS'05]. As a bonus, we also point out a simplification of a known optimal cache-oblivious (non-in-place) algorithm by Kumar and Ramos (2002) for 3-d convex hulls, and observe its applicability to 2-d segment intersection, extending a recent result for red/blue segment intersection by Arge, Molhave, and Zeh [ESA'08]. Our results are all obtained by standard random sampling techniques, with some interesting twists.