Affiliation:
1. Princeton University, Princeton, New Jersey
Abstract
In the late nineties, Erickson proved a remarkable lower bound on the decision tree complexity of one of the central problems of computational geometry: given
n
numbers, do any
r
of them add up to 0? His lower bound of Ω(
n
⌈
r
/2⌉
), for any fixed
r
, is optimal if the polynomials at the nodes are linear and at most
r
-variate. We generalize his bound to
s
-variate polynomials for
s
>
r
. Erickson's bound decays quickly as
r
grows and never reaches above pseudo-polynomial: we provide an exponential improvement. Our arguments are based on three ideas: (i) a geometrization of Erickson's proof technique; (ii) the use of error-correcting codes; and (iii) a tensor product construction for permutation matrices.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
19 articles.
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