An Efficient Multi-Dimensional Searching Technique and itsApplications

Authors:
K P Agarwal;Micha Sharir;Sivan Toledo
Affiliations:
-;-;-
Venue:
An Efficient Multi-Dimensional Searching Technique and itsApplications
Year:
1993

Citing 0
Cited 7

Computational geometry: a retrospective

STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Efficient algorithms for geometric optimization

ACM Computing Surveys (CSUR)
Decomposable multi-parameter matroid optimization problems

Theoretical Computer Science - Latin American theoretical informatics
Homology flows, cohomology cuts

Proceedings of the forty-first annual ACM symposium on Theory of computing
Maximum flows and parametric shortest paths in planar graphs

SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Modelling gateway placement in wireless networks: Geometric k-centres of unit disc graphs

Computational Geometry: Theory and Applications
Minimum enclosing circle of a set of fixed points and a mobile point

WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation

Quantified Score

Hi-index	0.08

Visualization

Abstract

This paper describes an improved algorithm for the multi-dimensional searching problem introduced by Megiddo. As a result, we obtain a $d^{O(d)} n$ time deterministic algorithms for linear programming in $\reals^d$ with $n$ constraints, for computing the Euclidean $1$-center of a set of $n$ points in $\Re^d$, for computing the minimum enclosing ellipsoid of a set of $n$ points in $\Re^d$, etc. Our techniques also improve the running time of known algorithms for a number of parametric graph searching problems, including that of finding zero cycles in dynamic graphs.