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COCO
2008
Springer
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14 years 2 months ago
Lower Bounds and Separations for Constant Depth Multilinear Circuits
We prove an exponential lower bound for the size of constant depth multilinear arithmetic circuits computing either the determinant or the permanent (a circuit is called multiline...
Ran Raz, Amir Yehudayoff
MFCS
1997
Springer
14 years 4 months ago
Resolution Proofs, Exponential Bounds, and Kolmogorov Complexity
We prove an exponential lower bound for the length of any resolution proof for the same set of clauses as the one used by Urquhart [13]. Our contribution is a signiļ¬cant simpliļ¬...
Uwe Schöning
COMPGEOM
2009
ACM
14 years 5 months ago
k-means requires exponentially many iterations even in the plane
The k-means algorithm is a well-known method for partitioning n points that lie in the d-dimensional space into k clusters. Its main features are simplicity and speed in practice....
Andrea Vattani
FSTTCS
2004
Springer
14 years 6 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 āˆˆ Rn such that the volume of their symmetric diļ¬€ere...
Luis Rademacher, Santosh Vempala