Related papers: Paths Beyond Local Search: A Nearly Tight Bound fo…

Grover's quantum search and its generalization, quantum amplitude amplification, provide quadratic advantage over classical algorithms for a diverse set of tasks, but are tricky to use without knowing beforehand what fraction $\lambda$ of…

As first-order optimization methods become the method of choice for solving large-scale optimization problems, optimization solvers based on first-order algorithms are being built. Such general-purpose solvers must robustly detect…

In large-scale applications, such as machine learning, it is desirable to design non-convex optimization algorithms with a high degree of parallelization. In this work, we study the adaptive complexity of finding a stationary point, which…

Local Search problem, which finds a local minimum of a black-box function on a given graph, is of both practical and theoretical importance to combinatorial optimization, complexity theory and many other areas in theoretical computer…

We study the problem of optimizing a function under a \emph{budgeted number of evaluations}. We only assume that the function is \emph{locally} smooth around one of its global optima. The difficulty of optimization is measured in terms of…

Let G=(V,E) be a finite graph, and f:V->N be any function. The Local Search problem consists in finding a local minimum of the function f on G, that is a vertex v such that f(v) is not larger than the value of f on the neighbors of v in G.…

Many computer graphics problems require computing geometric shapes subject to certain constraints. This often results in non-linear and non-convex optimization problems with globally coupled variables, which pose great challenge for…

Local search algorithms for combinatorial search problems frequently encounter a sequence of states in which it is impossible to improve the value of the objective function; moves through these regions, called plateau moves, dominate the…

We generalize the monotone local search approach of Fomin, Gaspers, Lokshtanov and Saurabh [J. ACM 2019], by establishing a connection between parameterized approximation and exponential-time approximation algorithms for monotone subset…

We propose stochastic optimization algorithms that can find local minima faster than existing algorithms for nonconvex optimization problems, by exploiting the third-order smoothness to escape non-degenerate saddle points more efficiently.…

Over the past 30 years numerous algorithms have been designed for symmetry breaking problems in the LOCAL model, such as maximal matching, MIS, vertex coloring, and edge-coloring. For most problems the best randomized algorithm is at least…

Fixed-point quantum search algorithms succeed at finding one of $M$ target items among $N$ total items even when the run time of the algorithm is longer than necessary. While the famous Grover's algorithm can search quadratically faster…

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…

A random local function defined by a $d$-ary predicate $P$ is one where each output bit is computed by applying $P$ to $d$ randomly chosen bits of its input. These represent natural distributions of instances for constraint satisfaction…

We provide simple but surprisingly useful direct product theorems for proving lower bounds on online algorithms with a limited amount of advice about the future. As a consequence, we are able to translate decades of research on randomized…

We propose a new algorithm that finds an $\varepsilon$-approximate fixed point of a smooth function from the $n$-dimensional $\ell_2$ unit ball to itself. We use the general framework of finding approximate solutions to a variational…

We continue the study of Genetic Algorithms (GA) on combinatorial optimization problems where the candidate solutions need to satisfy a balancedness constraint. It has been observed that the reduction of the search space size granted by…

Choosing a suitable algorithm from the myriads of different search heuristics is difficult when faced with a novel optimization problem. In this work, we argue that the purely academic question of what could be the best possible algorithm…

The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional…

In this paper, we present novel randomized algorithms for solving saddle point problems whose dual feasible region is given by the direct product of many convex sets. Our algorithms can achieve an ${\cal O}(1/N)$ and ${\cal O}(1/N^2)$ rate…