On k-hulls and related problems
SIAM Journal on Computing
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
A geometric consistency theorem for a symbolic perturbation scheme
Journal of Computer and System Sciences
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
Finding k points with minimum diameter and related problems
Journal of Algorithms
On levels in arrangements and Voronoi diagrams
Discrete & Computational Geometry
Points and triangles in the plane and halving planes in space
Discrete & Computational Geometry
A subexponential randomized simplex algorithm (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
A subexponential bound for linear programming
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
An efficient approach to removing geometric degeneracies
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Journal of Algorithms
An optimal algorithm for the (≤ k)-levels, with applications to separation and transversal problems
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Helly theorems and generalized linear programming
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Dehn-Sommerville relations, upper bound theorem, and levels in arrangements
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Counting triangle crossings and halving planes
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Constructing levels in arrangements and higher order Voronoi diagrams
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Iterated nearest neighbors and finding minimal polytypes
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
On linear-time deterministic algorithms for optimization problems in fixed dimension
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Computing the Smallest k-Enclosing Circle and Related Problems
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Static and Dynamic Algorithms for k-Point Clustering Problems
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
A Combinatorial Bound for Linear Programming and Related Problems
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
Dynamic Half-Space Range Reporting and Its Application
Dynamic Half-Space Range Reporting and Its Application
Bounded boxes, Hausdorff distance, and a new proof of an interesting Helly-type theorem
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Output-sensitive results on convex hulls, extreme points, and related problems
Proceedings of the eleventh annual symposium on Computational geometry
How to cut pseudo-parabolas into segments
Proceedings of the eleventh annual symposium on Computational geometry
Smallest Color-Spanning Objects
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
A Meeting Scheduling Problem Respecting Time and Space
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
A meeting scheduling problem respecting time and space
Geoinformatica
Approximating Points by a Piecewise Linear Function: II. Dealing with Outliers
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Generalized Convexity in Multiple View Geometry
Journal of Mathematical Imaging and Vision
Thin partitions: isoperimetric inequalities and a sampling algorithm for star shaped bodies
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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We investigate the problem of finding the best solution satisfying all but k of the given constraints, for an abstract class of optimization problems introduced by Sharir and Welzl—the so-called LP-type problems. We give a general algorithm and discuss its efficient implementations for specific geometric problems. For instance, for the problem of computing the smallest circle enclosing all but k of the given n points in the plane, we obtain an O(nlogn+k3n&egr;) algorithm; this improves previous results for k small compared ton but moderately growing.We also establish some results concerning general properties of LP-type problems.