Lower bounds for sorting of sums
Theoretical Computer Science
Linear decision trees: volume estimates and topological bounds
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Point location in arrangements of hyperplanes
Information and Computation
Algebraic decision trees and Euler characteristics
Theoretical Computer Science
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
A lower bound for randomized algebraic decision trees
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Perfect binary space partitions
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
Decision tree complexity and Betti numbers
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
New Lower Bounds for Convex Hull Problems in Odd Dimensions
SIAM Journal on Computing
A Polynomial Linear Search Algorithm for the n-Dimensional Knapsack Problem
Journal of the ACM (JACM)
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Finding an o(n2 log n) Algorithm Is Sometimes Hard
Proceedings of the 8th Canadian Conference on Computational Geometry
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Fast dimension reduction using Rademacher series on dual BCH codes
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Exact weight subgraphs and the k-sum conjecture
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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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.