Testing geometric convexity

Authors:
Luis Rademacher;Santosh Vempala
Affiliations:
Mathematics Department and CSAIL, MIT;Mathematics Department and CSAIL, MIT
Venue:
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Year:
2004

Citing 4
Cited 4

Randomized algorithms

Randomized algorithms
Property testing and its connection to learning and approximation

Journal of the ACM (JACM)
On Testing Convexity and Submodularity

SIAM Journal on Computing
Hit-and-run from a corner

STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing

Testing Euclidean spanners

ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Testing Euclidean spanners

Property testing
Testing Euclidean spanners

Property testing
A Randomized Cutting Plane Method with Probabilistic Geometric Convergence

SIAM Journal on Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the problem of determining whether a given set S in ${\mathbb R}^{n}$ is approximately convex, i.e., if there is a convex set $K \in {\mathbb R}^{n}$ such that the volume of their symmetric difference is at most ε vol(S) for some given ε. When the set is presented only by a membership oracle and a random oracle, we show that the problem can be solved with high probability using poly(n)(c/ε)n oracle calls and computation time. We complement this result with an exponential lower bound for the natural algorithm that tests convexity along “random” lines. We conjecture that a simple 2-dimensional version of this algorithm has polynomial complexity.