Hardness of approximate nearest neighbor search
A Rubinstein - Proceedings of the 50th annual ACM SIGACT …, 2018 - dl.acm.org
We prove conditional near-quadratic running time lower bounds for approximate
Bichromatic Closest Pair with Euclidean, Manhattan, Hamming, or edit distance. Specifically …
Bichromatic Closest Pair with Euclidean, Manhattan, Hamming, or edit distance. Specifically …
Distributed PCP theorems for hardness of approximation in P
A Abboud, A Rubinstein… - 2017 IEEE 58th Annual …, 2017 - ieeexplore.ieee.org
We present a new distributed model of probabilistically checkable proofs (PCP). A satisfying
assignment x∈{0, 1} n to a CNF formula φ is shared between two parties, where Alice …
assignment x∈{0, 1} n to a CNF formula φ is shared between two parties, where Alice …
Johnson Coverage Hypothesis: Inapproximability of k-means and k-median in ℓp-metrics
V Cohen-Addad, E Lee - Proceedings of the 2022 Annual ACM-SIAM …, 2022 - SIAM
k-median and k-means are the two most popular objectives for clustering algorithms.
Despite intensive effort, a good understanding of the approximability of these objectives …
Despite intensive effort, a good understanding of the approximability of these objectives …
Inapproximability of clustering in lp metrics
V Cohen-Addad, CS Karthik - 2019 IEEE 60th Annual …, 2019 - ieeexplore.ieee.org
Proving hardness of approximation for min-sum objectives is an infamous challenge. For
classic problems such as the Traveling Salesman problem, the Steiner tree problem, or the k …
classic problems such as the Traveling Salesman problem, the Steiner tree problem, or the k …
On the hardness of approximate and exact (bichromatic) maximum inner product
L Chen - arXiv preprint arXiv:1802.02325, 2018 - arxiv.org
In this paper we study the (Bichromatic) Maximum Inner Product Problem (Max-IP), in which
we are given sets $ A $ and $ B $ of vectors, and the goal is to find $ a\in A $ and $ b\in B …
we are given sets $ A $ and $ B $ of vectors, and the goal is to find $ a\in A $ and $ b\in B …
On closest pair in euclidean metric: Monochromatic is as hard as bichromatic
CS Karthik, P Manurangsi - Combinatorica, 2020 - Springer
Given a set of n points in ℝ d, the (monochromatic) Closest Pair problem asks to find a pair
of distinct points in the set that are closest in the ℓ p-metric. Closest Pair is a fundamental …
of distinct points in the set that are closest in the ℓ p-metric. Closest Pair is a fundamental …
On the quantum complexity of closest pair and related problems
The closest pair problem is a fundamental problem of computational geometry: given a set of
$ n $ points in a $ d $-dimensional space, find a pair with the smallest distance. A classical …
$ n $ points in a $ d $-dimensional space, find a pair with the smallest distance. A classical …
Impossibility results for grammar-compressed linear algebra
Impossibility Results for Grammar-Compressed Linear Algebra Page 1 Impossibility Results
for Grammar-Compressed Linear Algebra Amir Abboud IBM Almaden Research Center amir.abboud@gmail.com …
for Grammar-Compressed Linear Algebra Amir Abboud IBM Almaden Research Center amir.abboud@gmail.com …
On efficient low distortion ultrametric embedding
V Cohen-Addad, CS Karthik… - … on Machine Learning, 2020 - proceedings.mlr.press
A classic problem in unsupervised learning and data analysis is to find simpler and easy-to-
visualize representations of the data that preserve its essential properties. A widely-used …
visualize representations of the data that preserve its essential properties. A widely-used …
Bayes security: A not so average metric
K Chatzikokolakis, G Cherubin… - 2023 IEEE 36th …, 2023 - ieeexplore.ieee.org
Security system designers favor worst-case security metrics, such as those derived from
differential privacy (DP), due to the strong guarantees they provide. On the downside, these …
differential privacy (DP), due to the strong guarantees they provide. On the downside, these …