Related papers: Approximate $\mathrm{CVP}_{p}$ in time $2^{0.802 \…

We study streaming algorithms for the $\ell_p$ subspace approximation problem. Given points $a_1, \ldots, a_n$ as an insertion-only stream and a rank parameter $k$, the $\ell_p$ subspace approximation problem is to find a $k$-dimensional…

Given a set of $n$ sites from $\mathbb{R}^d$, each having some positive weight factor, the Multiplicatively Weighted Voronoi Diagram is a subdivision of space that associates each cell to the site whose weighted Euclidean distance is…

Given a graph $G = (V, E)$, we wish to compute a spanning tree whose maximum vertex degree, i.e. tree degree, is as small as possible. Computing the exact optimal solution is known to be NP-hard, since it generalizes the Hamiltonian path…

We consider the Low Rank Approximation problem, where the input consists of a matrix $A \in \mathbb{R}^{n_R \times n_C}$ and an integer $k$, and the goal is to find a matrix $B$ of rank at most $k$ that minimizes $\| A - B \|_0$, which is…

The Integer Programming Problem (IP) for a polytope P \subseteq R^n is to find an integer point in P or decide that P is integer free. We give an algorithm for an approximate version of this problem, which correctly decides whether P…

We propose a Projected Proximal Point Algorithm (ProPPA) for solving a class of optimization problems. The algorithm iteratively computes the proximal point of the last estimated solution projected into an affine space which itself is…

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 study the worst-case approximation of multivariate periodic functions from the weighted Korobov space $H_{d,\alpha,\gamma}$ with smoothness $\alpha>1/2$ in the Lebesgue norm $L_p([0,1]^d)$ for $1\le p\le\infty$. We analyze a \emph{median…

This paper investigates the approximability of the Longest Common Subsequence (LCS) problem. The fastest algorithm for solving the LCS problem exactly runs in essentially quadratic time in the length of the input, and it is known that under…

Edit distance is a measure of similarity of two strings based on the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. The edit distance can be computed exactly using a…

We consider a natural generalization of the Partial Vertex Cover problem. Here an instance consists of a graph G = (V,E), a positive cost function c: V-> Z^{+}, a partition $P_1,..., P_r$ of the edge set $E$, and a parameter $k_i$ for each…

We study approximation algorithms for several variants of the MaxCover problem, with the focus on algorithms that run in FPT time. In the MaxCover problem we are given a set N of elements, a family S of subsets of N, and an integer K. The…

In this work we consider the problem of maximizing the PageRank of a given target node in a graph by adding $k$ new links. We consider the case that the new links must point to the given target node (backlinks). Previous work shows that…

In Maximum $k$-Vertex Cover (Max $k$-VC), the input is an edge-weighted graph $G$ and an integer $k$, and the goal is to find a subset $S$ of $k$ vertices that maximizes the total weight of edges covered by $S$. Here we say that an edge is…

We consider the problem of finding the optimal coefficient vector that maximizes the computation rate at a relay in the compute-and-forward scheme. Based on the idea of sphere decoding, we propose a highly efficient algorithm that finds the…

In this paper, we study the Maximum Profit Pick-up Problem with Time Windows and Capacity Constraint (MP-PPTWC). Our main results are 3 polynomial time algorithms, all having constant approximation factors. The first algorithm has an…

Given an undirected graph with edge costs and edge demands, the Capacitated Arc Routing problem (CARP) asks for minimum-cost routes for equal-capacity vehicles so as to satisfy all demands. Constant-factor polynomial-time approximation…

We study approximation algorithms for the socially fair $(\ell_p, k)$-clustering problem with $m$ groups, whose special cases include the socially fair $k$-median ($p=1$) and socially fair $k$-means ($p=2$) problems. We present (1) a…

We propose an algorithm with expected complexity of $\bigO(n\log n)$ arithmetic operations to solve a special shortest vector problem arising in computer-and-forward design, where $n$ is the dimension of the channel vector. This algorithm…

Given a matrix $A\in \mathbb{R}^{n\times d}$ and a vector $b\in \mathbb{R}^n$, we consider the regression problem with $\ell_\infty$ guarantees: finding a vector $x'\in \mathbb{R}^d$ such that $ \|x'-x^*\|_\infty \leq…