Efficient searching with linear constraints
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Results on k-sets and j-facets via continuous motion
Proceedings of the fourteenth annual symposium on Computational geometry
Proceedings of the fourteenth annual symposium on Computational geometry
Parametric polymatroid optimization and its geometric applications
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Finding an Optimal Path without Growing the Tree
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Finding an optimal path without growing the tree
Journal of Algorithms
Decision-making based on approximate and smoothed Pareto curves
Theoretical Computer Science
Algorithms for bivariate zonoid depth
Computational Geometry: Theory and Applications
An improved bound for k-sets in four dimensions
Combinatorics, Probability and Computing
Decision making based on approximate and smoothed pareto curves
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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We prove an O(nk/sup 1/3/) upper bound for planar k-sets. This is the first considerable improvement on this bound after its early solutions approximately twenty seven years ago. Our proof technique also applies to improve the current bounds on the combinatorial complexities of k-levels in arrangements of line segments, k convex polygons in the union of n lines, parametric minimum spanning trees and parametric matroids in general.