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We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank $f$. This problem is equivalent to the Minimum Weight Set Cover Problem in which the frequency of every…
Universal approximation theory offers a foundational framework to verify neural network expressiveness, enabling principled utilization in real-world applications. However, most existing theoretical constructions are established by…
This paper presents an approximation algorithm for finding a shortest path between two points $s$ and $t$ in a weighted planar subdivision $\PS$. Each face $f$ of $\PS$ is associated with a weight $w_f$, and the cost of travel along a line…
Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, which is how to find a good regularizer. While total…
This paper presents a novel method for generating a single polynomial approximation that produces correctly rounded results for all inputs of an elementary function for multiple representations. The generated polynomial approximation has…
The Virtual Network Embedding Problem (VNEP) considers the efficient allocation of resources distributed in a substrate network to a set of request networks. Many existing works discuss either heuristics or exact algorithms, resulting in a…
We consider the global minimization of smooth functions based solely on function evaluations. Algorithms that achieve the optimal number of function evaluations for a given precision level typically rely on explicitly constructing an…
With the increasing growth of technology and the entrance into the digital age, we have to handle a vast amount of information every time which often presents difficulties. So, the digital information must be stored and retrieved in an…
The problem of maximizing the $p$-th power of a $p$-norm over a halfspace-presented polytope in $\R^d$ is a convex maximization problem which plays a fundamental role in computational convexity. It has been shown in 1986 that this problem…
Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By…
We investigate the existence of approximation algorithms for maximization of submodular functions, that run in fixed parameter tractable (FPT) time. Given a non-decreasing submodular set function $v: 2^X \to \mathbb{R}$ the goal is to…
A local algorithm is a distributed algorithm where each node must operate solely based on the information that was available at system startup within a constant-size neighbourhood of the node. We study the applicability of local algorithms…
We study the problem of approximating Hamming distance in sublinear time under property-preserving hashing (PPH), where only hashed representations of inputs are available. Building on the threshold evaluation framework of Fleischhacker,…
This paper presents an algorithm for the efficient approximation of the saddle-extremum persistence diagram of a scalar field. Vidal et al. introduced recently a fast algorithm for such an approximation (by interrupting a progressive…
The classical low rank approximation problem is to find a rank $k$ matrix $UV$ (where $U$ has $k$ columns and $V$ has $k$ rows) that minimizes the Frobenius norm of $A - UV$. Although this problem can be solved efficiently, we study an…
We study approximation algorithms for the following three string measures that are widely used in practice: edit distance (ED), longest common subsequence (LCS), and longest increasing sequence (LIS). All three problems can be solved…
We consider the inverse problem of reconstructing an unknown function $u$ from a finite set of measurements, under the assumption that $u$ is the trajectory of a transport-dominated problem with unknown input parameters. We propose an…
We initiate a systematic study of tolerant testers of image properties or, equivalently, algorithms that approximate the distance from a given image to the desired property (that is, the smallest fraction of pixels that need to change in…
For any two point sets $A,B \subset \mathbb{R}^d$ of size up to $n$, the Chamfer distance from $A$ to $B$ is defined as $\text{CH}(A,B)=\sum_{a \in A} \min_{b \in B} d_X(a,b)$, where $d_X$ is the underlying distance measure (e.g., the…
In the paper "The best m-term approximation and greedy algorithms" (V. N. Temlyakov), an error bound for a near best m-term approximation of a function g in L^p([0,1]^d) is provided, using a basis L^p-equivalent to the Haar system, where p…