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The problem of identifying a planted assignment given a random $k$-SAT formula consistent with the assignment exhibits a large algorithmic gap: while the planted solution becomes unique and can be identified given a formula with $O(n\log…
Spike sorting is a class of algorithms used in neuroscience to attribute the time occurences of particular electric signals, called action potential or spike, to neurons. We rephrase this problem as a particular optimization problem : Lasso…
Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…
Given $k$ collections of 2SAT clauses on the same set of variables $V$, can we find one assignment that satisfies a large fraction of clauses from each collection? We consider such simultaneous constraint satisfaction problems, and design…
An influential result by Dor, Halperin, and Zwick (FOCS 1996, SICOMP 2000) implies an algorithm that can compute approximate shortest paths for all vertex pairs in $\tilde{O}(n^{2+O\left(\frac{1}{k}\right )})$ time, ensuring that the output…
In the discrete $k$-center problem, we are given a metric space $(P,\texttt{dist})$ where $|P|=n$ and the goal is to select a set $C\subseteq P$ of $k$ centers which minimizes the maximum distance of a point in $P$ from its nearest center.…
Let ${\cal G}$ be a minor-closed graph class and let $G$ be an $n$-vertex graph. We say that $G$ is a $k$-apex of ${\cal G}$ if $G$ contains a set $S$ of at most $k$ vertices such that $G\setminus S$ belongs to ${\cal G}$. Our first result…
Confidence intervals are a standard technique for analyzing data. When applied to time series, confidence intervals are computed for each time point separately. Alternatively, we can compute confidence bands, where we are required to find…
The sum of radii problem ($k$-MSR) asks, given a metric space on $n$ points, to place $k$ balls covering all points so as to minimize the sum of their radii. Despite extensive study from the perspectives of approximation and parameterized…
We consider the stochastic $k$-TSP problem where rewards at vertices are random and the objective is to minimize the expected length of a tour that collects reward $k$. We present an adaptive $O(\log k)$-approximation algorithm, and a…
One of the most fundamental problems in Computer Science is the Knapsack problem. Given a set of n items with different weights and values, it asks to pick the most valuable subset whose total weight is below a capacity threshold T. Despite…
We study the classic NP-Hard problem of finding the maximum $k$-set coverage in the data stream model: given a set system of $m$ sets that are subsets of a universe $\{1,\ldots,n \}$, find the $k$ sets that cover the most number of distinct…
Let $A$ and $B$ be two point sets in the plane of sizes $r$ and $n$ respectively (assume $r \leq n$), and let $k$ be a parameter. A matching between $A$ and $B$ is a family of pairs in $A \times B$ so that any point of $A \cup B$ appears in…
We study the problem of metrical service systems with multiple servers (MSSMS), which generalizes two well-known problems -- the $k$-server problem, and metrical service systems. The MSSMS problem is to service requests, each of which is an…
Lattices are very important objects in the effort to construct cryptographic primitives that are secure against quantum attacks. A central problem in the study of lattices is that of finding the shortest non-zero vector in the lattice.…
We introduce here a rewrite system in the group of unimodular matrices, \emph{i.e.}, matrices with integer entries and with determinant equal to $\pm 1$. We use this rewrite system to precisely characterize the mechanism of the Gaussian…
We prove that some exact geometric pattern matching problems reduce in linear time to $k$-SUM when the pattern has a fixed size $k$. This holds in the real RAM model for searching for a similar copy of a set of $k\geq 3$ points within a set…
The lower and the upper irredundance numbers of a graph $G$, denoted $ir(G)$ and $IR(G)$ respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph parameters. It is a…
In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…
We introduce a novel scheme for choosing the regularization parameter in high-dimensional linear regression with Lasso. This scheme, inspired by Lepski's method for bandwidth selection in non-parametric regression, is equipped with both…