Computational geometry: an introduction
Computational geometry: an introduction
The ultimate planar convex hull algorithm
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
Load balancing requires &OHgr;(log*n) expected time
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Output-sensitive results on convex hulls, extreme points, and related problems
Proceedings of the eleventh annual symposium on Computational geometry
Optimal parallel randomized renaming
Information Processing Letters
Optimal, output-sensitive algorithms for constructing planar hulls in parallel
Computational Geometry: Theory and Applications
Fast deterministic processor allocation
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Output-sensitive construction of polytopes in four dimensions and clipped Voronoi diagrams in three
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
On Finding the Maxima of a Set of Vectors
Journal of the ACM (JACM)
A Lower Bound to Finding Convex Hulls
Journal of the ACM (JACM)
Output-size sensitive algorithms for finding maximal vectors
SCG '85 Proceedings of the first annual symposium on Computational geometry
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Optimal deterministic approximate parallel prefix sums and their applications
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Distribution-Sensitive construction of minimum-redundancy prefix codes
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
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We investigate a new paradigm of algorithm design for geometric problems that can be termed distribution-sensitive. Our notion of distribution is more combinatorial in nature than spatial. We illustrate this on problems like planar-hulls and 2D-maxima where some of the previously known output-sensitive algorithms are recast in this setting. In a number of cases, the distribution-sensitive analysis yields superior results for the above problems. Moreover these bounds are shown to be tight in the linear decision tree model.Our approach owes its spirit to the results known for sorting multisets and we exploit this relationship further to derive fast and efficient parallel algorithms for sorting multisets along with the geometric problems.