Related papers: Improved Analysis of a Max Cut Algorithm Based on …
We consider the problem of partitioning the node set of a graph into $k$ sets of given sizes in order to \emph{minimize the cut} obtained using (removing) the $k$-th set. If the resulting cut has value $0$, then we have obtained a vertex…
We consider the problem of estimating the value of MAX-CUT in a graph in the streaming model of computation. At one extreme, there is a trivial $2$-approximation for this problem that uses only $O(\log n)$ space, namely, count the number of…
Partitioning and grouping of similar objects plays a fundamental role in image segmentation and in clustering problems. In such problems a typical goal is to group together similar objects, or pixels in the case of image processing. At the…
Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity…
We consider the selective graph coloring problem, which is a generalization of the classical graph coloring problem. Given a graph together with a partition of its vertex set into clusters, we want to choose exactly one vertex per cluster…
We revisit two NP-hard geometric partitioning problems - convex decomposition and surface approximation. Building on recent developments in geometric separators, we present quasi-polynomial time algorithms for these problems with improved…
We investigate semi-streaming algorithms for the Traveling Salesman Problem (TSP). Specifically, we focus on a variant known as the $(1,2)$-TSP, where the distances between any two vertices are either one or two. Our primary emphasis is on…
Max-cut, clustering, and many other partitioning problems that are of significant importance to machine learning and other scientific fields are NP-hard, a reality that has motivated researchers to develop a wealth of approximation…
Segmenting an image into multiple components is a central task in computer vision. In many practical scenarios, prior knowledge about plausible components is available. Incorporating such prior knowledge into models and algorithms for image…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
In this work, we develop a framework aiming at designing quantum algorithms for combinatorial optimization problems while providing theoretical guarantees on their approximation ratios. The principal innovative aspect of our work is the…
In combinatorial optimization, partial variable assignments are called persistent if they agree with some optimal solution. We propose persistency criteria for the multicut and max-cut problem as well as fast combinatorial routines to…
We examine the problem of approximating a positive, semidefinite matrix $\Sigma$ by a dyad $xx^T$, with a penalty on the cardinality of the vector $x$. This problem arises in sparse principal component analysis, where a decomposition of…
We study range-searching for colored objects, where one has to count (approximately) the number of colors present in a query range. The problems studied mostly involve orthogonal range-searching in two and three dimensions, and the dual…
This paper establishes a nearly optimal algorithm for estimating the frequencies and amplitudes of a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery…
MAX NAE-SAT is a natural optimization problem, closely related to its better-known relative MAX SAT. The approximability status of MAX NAE-SAT is almost completely understood if all clauses have the same size $k$, for some $k\ge 2$. We…
For some $\epsilon > 10^{-36}$ we give a randomized $3/2-\epsilon$ approximation algorithm for metric TSP.
We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…
We consider least squares approximation of a function of one variable by a continuous, piecewise-linear approximand that has a small number of breakpoints. This problem was notably considered by Bellman who proposed an approximate algorithm…
In this paper we present a first-order method that admits near-optimal convergence rates for convex/concave min-max problems while requiring a simple and intuitive analysis. Similarly to the seminal work of Nemirovski and the recent…