On some fine-grained questions in algorithms and complexity
VV Williams - Proceedings of the international congress of …, 2018 - World Scientific
In recent years, a new “fine-grained” theory of computational hardness has been developed,
based on “fine-grained reductions” that focus on exact running times for problems …
based on “fine-grained reductions” that focus on exact running times for problems …
Bypass exponential time preprocessing: Fast neural network training via weight-data correlation preprocessing
Over the last decade, deep neural networks have transformed our society, and they are
already widely applied in various machine learning applications. State-of-the-art deep …
already widely applied in various machine learning applications. State-of-the-art deep …
Tight hardness for shortest cycles and paths in sparse graphs
Fine-grained reductions have established equivalences between many core problems with
Õ (n 3)-time algorithms on n-node weighted graphs, such as Shortest Cycle, All-Pairs …
Õ (n 3)-time algorithms on n-node weighted graphs, such as Shortest Cycle, All-Pairs …
Training overparametrized neural networks in sublinear time
The success of deep learning comes at a tremendous computational and energy cost, and
the scalability of training massively overparametrized neural networks is becoming a real …
the scalability of training massively overparametrized neural networks is becoming a real …
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 …
SETH-based lower bounds for subset sum and bicriteria path
A Abboud, K Bringmann, D Hermelin… - ACM Transactions on …, 2022 - dl.acm.org
Subset Sumand k-SAT are two of the most extensively studied problems in computer
science, and conjectures about their hardness are among the cornerstones of fine-grained …
science, and conjectures about their hardness are among the cornerstones of fine-grained …
On the fine-grained complexity of one-dimensional dynamic programming
M Künnemann, R Paturi, S Schneider - arxiv preprint arxiv:1703.00941, 2017 - arxiv.org
In this paper, we investigate the complexity of one-dimensional dynamic programming, or
more specifically, of the Least-Weight Subsequence (LWS) problem: Given a sequence of …
more specifically, of the Least-Weight Subsequence (LWS) problem: Given a sequence of …
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 …
An equivalence class for orthogonal vectors
L Chen, R Williams - Proceedings of the Thirtieth Annual ACM-SIAM …, 2019 - SIAM
Abstract The Orthogonal Vectors problem (OV) asks: given n vectors in {0, 1} O (log n), are
two of them orthogonal? OV is easily solved in O (n 2 log n) time, and it is a central problem …
two of them orthogonal? OV is easily solved in O (n 2 log n) time, and it is a central problem …
Hitting set enumeration with partial information for unique column combination discovery
Unique column combinations (UCCs) are a fundamental concept in relational databases.
They identify entities in the data and support various data management activities. Still, UCCs …
They identify entities in the data and support various data management activities. Still, UCCs …