Related papers: Fine-Grained Cryptanalysis: Tight Conditional Boun…
We design the first efficient sensitivity oracles and dynamic algorithms for a variety of parameterized problems. Our main approach is to modify the algebraic coding technique from static parameterized algorithm design, which had not…
We prove lower bounds for higher-order methods in smooth non-convex finite-sum optimization. Our contribution is threefold: We first show that a deterministic algorithm cannot profit from the finite-sum structure of the objective, and that…
We study the unsorted database search problem with items $N$ from the viewpoint of unitary discrimination. Instead of considering the famous $O(\sqrt{N})$ Grover's the bounded-error algorithm for the original problem, we seek for the…
We give a near-optimal quantum algorithm for the longest common substring (LCS) problem between two run-length encoded (RLE) strings, with the assumption that the prefix-sums of the run-lengths are given. Our algorithm costs…
Discovering dense subgraphs and understanding the relations among them is a fundamental problem in graph mining. We want to not only identify dense subgraphs, but also build a hierarchy among them (e.g., larger but sparser subgraphs formed…
The classical coding theorem in Kolmogorov complexity states that if an $n$-bit string $x$ is sampled with probability $\delta$ by an algorithm with prefix-free domain then K$(x) \leq \log(1/\delta) + O(1)$. In a recent work, Lu and…
We give a stochastic optimization algorithm that solves a dense $n\times n$ real-valued linear system $Ax=b$, returning $\tilde x$ such that $\|A\tilde x-b\|\leq \epsilon\|b\|$ in time: $$\tilde O((n^2+nk^{\omega-1})\log1/\epsilon),$$ where…
We study a broad class of algorithmic problems with an "additive flavor" such as computing sumsets, 3SUM, Subset Sum and geometric pattern matching. Our starting point is that these problems can often be solved efficiently for integers,…
We give oracle inequalities on procedures which combines quantization and variable selection via a weighted Lasso $k$-means type algorithm. The results are derived for a general family of weights, which can be tuned to size the influence of…
Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees,…
In parameterized complexity, it is a natural idea to consider different generalizations of classic problems. Usually, such generalization are obtained by introducing a "relaxation" variable, where the original problem corresponds to setting…
Motivated by many applications, we study clustering with a faulty oracle. In this problem, there are $n$ items belonging to $k$ unknown clusters, and the algorithm is allowed to ask the oracle whether two items belong to the same cluster or…
We establish two results regarding the query complexity of bounded-error randomized algorithms. * Bounded-error separation theorem. There exists a total function $f : \{0,1\}^n \to \{0,1\}$ whose $\epsilon$-error randomized query complexity…
Tensor rank and low-rank tensor decompositions have many applications in learning and complexity theory. Most known algorithms use unfoldings of tensors and can only handle rank up to $n^{\lfloor p/2 \rfloor}$ for a $p$-th order tensor in…
The random $k$-XORSAT problem is a random constraint satisfaction problem of $n$ Boolean variables and $m=rn$ clauses, which a random instance can be expressed as a $G\mathbb{F}(2)$ linear system of the form $Ax=b$, where $A$ is a random $m…
SARRIGUREN, a new complete algorithm for SAT based on counting clauses (which is valid also for Unique-SAT and #SAT) is described, analyzed and tested. Although existing complete algorithms for SAT perform slower with clauses with many…
Clustering plays a crucial role in computer science, facilitating data analysis and problem-solving across numerous fields. By partitioning large datasets into meaningful groups, clustering reveals hidden structures and relationships within…
In this work, we study a range of constrained versions of the $k$-supplier and $k$-center problems such as: capacitated, fault-tolerant, fair, etc. These problems fall under a broad framework of constrained clustering. A unified framework…
We use the Sum of Squares method to develop new efficient algorithms for learning well-separated mixtures of Gaussians and robust mean estimation, both in high dimensions, that substantially improve upon the statistical guarantees achieved…
Computing the convolution $A\star B$ of two length-$n$ vectors $A,B$ is an ubiquitous computational primitive. Applications range from string problems to Knapsack-type problems, and from 3SUM to All-Pairs Shortest Paths. These applications…