Algorithms for the Frame of a Finitely Generated Unbounded Polyhedron
INFORMS Journal on Computing
Removing redundant quadratic constraints
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
An Algorithm for Data Envelopment Analysis
INFORMS Journal on Computing
Orthogonal range searching on the RAM, revisited
Proceedings of the twenty-seventh annual symposium on Computational geometry
A fast algorithm for three-dimensional layers of maxima problem
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Maxima-finding algorithms for multidimensional samples: A two-phase approach
Computational Geometry: Theory and Applications
Competing output-sensitive frame algorithms
Computational Geometry: Theory and Applications
Point sets and frame algorithms in management
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
An Algorithm for Data Envelopment Analysis
INFORMS Journal on Computing
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A simple idea for speeding up the computation of extrema of a partially ordered set turns out to have a number of interesting applications in geometric algorithms; the resulting algorithms generally replace an appearance of the input size n in the running time by an output size A/spl les/n. In particular, the A coordinate-wise minima of a set of n points in R/sup d/ can be found by an algorithm needing O(nA) time. Given n points uniformly distributed in the unit square, the algorithm needs n+O(n/sup 5/8/) point comparisons on average. Given a set of n points in R/sup d/, another algorithm can find its A extreme points in O(nA) time. Thinning for nearest-neighbor classification can be done in time O(n log n)/spl Sigma//sub i/ A/sub i/n/sub i/, finding the A/sub i/ irredundant points among n/sub i/ points for each class i, where n=/spl Sigma//sub i/ n/sub i/ is the total number of input points. This sharpens a more obvious O(n/sup 3/) algorithm, which is also given here. Another algorithm is given that needs O(n) space to compute the convex hull of n points in O(nA) time. Finally, a new randomized algorithm finds the convex hull of n points in O(n log A) expected time, under the condition that a random subset of the points of size r has expected hull complexity O(r). All but the last of these algorithms has polynomial dependence on the dimension d, except possibly for linear programming.