Related papers: Optimal Monotone Depth-Three Circuit Lower Bounds …
Very recently, Khoury and Schild [FOCS 2025] showed that any randomized LOCAL algorithm that solves maximal matching requires $\Omega(\min\{\log \Delta, \log_\Delta n\})$ rounds, where $n$ is the number of nodes in the graph and $\Delta$ is…
In this paper we present three different results dealing with the number of $(\leq k)$-facets of a set of points: 1. We give structural properties of sets in the plane that achieve the optimal lower bound $3\binom{k+2}{2}$ of $(\leq…
The classic lower bound of Kuhn, Moscibroda and Wattenhofer [JACM 2016] states that approximate maximum matching and approximate vertex cover (among other problems) in the LOCAL model require $\Omega(\min\{\sqrt{\frac{\log n}{\log\log n}},…
The problem of minimizing the Potts energy function frequently occurs in computer vision applications. One way to tackle this NP-hard problem was proposed by Kovtun [19,20]. It identifies a part of an optimal solution by running $k$ maxflow…
The last five years of research on distributed graph algorithms have seen huge leaps of progress, both regarding algorithmic improvements and impossibility results: new strong lower bounds have emerged for many central problems and…
We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
In this paper, we present a low-diameter decomposition algorithm in the LOCAL model of distributed computing that succeeds with probability $1 - 1/poly(n)$. Specifically, we show how to compute an $\left(\epsilon, O\left(\frac{\log…
Let $\Phi$ be a random $k$-CNF formula on $n$ variables and $m$ clauses, where each clause is a disjunction of $k$ literals chosen independently and uniformly. Our goal is to sample an approximately uniform solution of $\Phi$ (or…
We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n + log log (1/epsilon)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2^n…
In this work, we present a fast distributed algorithm for local potential problems: these are graph problems where the task is to find a locally optimal solution where no node can unilaterally improve the utility in its local neighborhood…
We consider the problem of finding a near ground state of a $p$-spin model with Rademacher couplings by means of a low-depth circuit. As a direct extension of the authors' recent work [Gamarnik, Jagannath, Wein 2020], we establish that any…
In this paper we design a new primal-dual algorithm for the classic discrete optimization problem of maximizing a monotone submodular function subject to a cardinality constraint achieving the optimal approximation of $(1-1/e)$. This…
Large-scale subset selection asks for a small useful set of examples, features, sensors, seed users, or context passages from an enormous ground set. Submodular maximization is a canonical model for such diminishing-returns problems, but…
We develop efficient randomized algorithms to solve the black-box reconstruction problem for polynomials over finite fields, computable by depth three arithmetic circuits with alternating addition/multiplication gates, such that output gate…
We study the \emph{multiterminal cut} problem, which, given an $n$-vertex graph whose edges are integer-weighted and a set of terminals, asks for a partition of the vertex set such that each terminal is in a distinct part, and the total…
Among the cost metrics characterizing a quantum circuit, the $T$-count stands out as one of the most crucial as its minimization is particularly important in various areas of quantum computation such as fault-tolerant quantum computing and…
Clustering is a fundamental problem in unsupervised learning, and has been studied widely both as a problem of learning mixture models and as an optimization problem. In this paper, we study clustering with respect the emph{k-median}…
In 2009, Roeglin and Teng showed that the smoothed number of Pareto optimal solutions of linear multi-criteria optimization problems is polynomially bounded in the number $n$ of variables and the maximum density $\phi$ of the semi-random…
Submodular maximization is a general optimization problem with a wide range of applications in machine learning (e.g., active learning, clustering, and feature selection). In large-scale optimization, the parallel running time of an…