3 research outputs found
Improved Inapproximability of VC Dimension and Littlestone's Dimension via (Unbalanced) Biclique
Full text linkWe study the complexity of computing (and approximating) VC Dimension and
Littlestone's Dimension when we are given the concept class explicitly. We give
a simple reduction from Maximum (Unbalanced) Biclique problem to approximating
VC Dimension and Littlestone's Dimension. With this connection, we derive a
range of hardness of approximation results and running time lower bounds. For
example, under the (randomized) Gap-Exponential Time Hypothesis or the
Strongish Planted Clique Hypothesis, we show a tight inapproximability result:
both dimensions are hard to approximate to within a factor of in
polynomial-time. These improve upon constant-factor inapproximability results
from [Manurangsi and Rubinstein, COLT 2017].Comment: To appear in ITCS 202
