Search Results for author: Thijs Laarhoven

Found 4 papers, 2 papers with code

Polytopes, lattices, and spherical codes for the nearest neighbor problem

no code implementations10 Jul 2019 Thijs Laarhoven

In three and four dimensions, we numerically find that the tetrahedron, $5$-cell, and $16$-cell achieve the best query exponents, while in five or more dimensions orthoplices appear to outperform regular simplices, as well as the root lattice families $A_k$ and $D_k$.


Evolutionary techniques in lattice sieving algorithms

no code implementations10 Jul 2019 Thijs Laarhoven

Lattice-based cryptography has recently emerged as a prominent candidate for secure communication in the quantum age.

Hypercube LSH for approximate near neighbors

1 code implementation19 Feb 2017 Thijs Laarhoven

A celebrated technique for finding near neighbors for the angular distance involves using a set of \textit{random} hyperplanes to partition the space into hash regions [Charikar, STOC 2002].

Data Structures and Algorithms Computational Complexity Computational Geometry Cryptography and Security

Practical and Optimal LSH for Angular Distance

1 code implementation NeurIPS 2015 Alexandr Andoni, Piotr Indyk, Thijs Laarhoven, Ilya Razenshteyn, Ludwig Schmidt

Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.

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