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FSTTCS
2004
Springer

Testing Geometric Convexity

11 years 10 months ago
Testing Geometric Convexity
We consider the problem of determining whether a given set S in Rn is approximately convex, i.e., if there is a convex set K ∈ Rn such that the volume of their symmetric difference is at most vol(S) for some given . 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/ )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.
Luis Rademacher, Santosh Vempala
Added 01 Jul 2010
Updated 01 Jul 2010
Type Conference
Year 2004
Where FSTTCS
Authors Luis Rademacher, Santosh Vempala
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