Related papers: Improved Combinatorial Approximations for Weighted…
The Bin Packing Problem is one of the most important optimization problems. In recent years, due to its NP-hard nature, several approximation algorithms have been presented. It is proved that the best algorithm for the Bin Packing Problem…
We study the Euclidean minimum weight perfect matching problem for $n$ points in the plane. It is known that any deterministic approximation algorithm whose approximation ratio depends only on $n$ requires at least $\Omega(n \log n)$ time.…
Many application areas collect unstructured trajectory data. In subtrajectory clustering, one is interested to find patterns in this data using a hybrid combination of segmentation and clustering. We analyze two variants of this problem…
We study two generalizations of classic clustering problems called dynamic ordered $k$-median and dynamic $k$-supplier, where the points that need clustering evolve over time, and we are allowed to move the cluster centers between…
We study Clustered Planarity with Linear Saturators, which is the problem of augmenting an $n$-vertex planar graph whose vertices are partitioned into independent sets (called clusters) with paths - one for each cluster - that connect all…
Correlation clustering is a central topic in unsupervised learning, with many applications in ML and data mining. In correlation clustering, one receives as input a signed graph and the goal is to partition it to minimize the number of…
The distinguishable cluster approximation applied to coupled cluster doubles equations greatly improves absolute and relative energies. We apply the same approximation to the triples equations and demonstrate that it can also improve…
In this paper, we present a cluster algorithm for the numerical simulations of non-additive hard-core mixtures. This algorithm allows one to simulate and equilibrate systems with a number of particles two orders of magnitude larger than…
In consensus clustering, a clustering algorithm is used in combination with a subsampling procedure to detect stable clusters. Previous studies on both simulated and real data suggest that consensus clustering outperforms native algorithms.…
Clustering, a fundamental task in data science and machine learning, groups a set of objects in such a way that objects in the same cluster are closer to each other than to those in other clusters. In this paper, we consider a well-known…
In this paper we consider the classic scheduling problem of minimizing total weighted completion time on unrelated machines when jobs have release times, i.e, $R | r_{ij} | \sum_j w_j C_j$ using the three-field notation. For this problem, a…
We study the problem of list-decodable mean estimation, where an adversary can corrupt a majority of the dataset. Specifically, we are given a set $T$ of $n$ points in $\mathbb{R}^d$ and a parameter $0< \alpha <\frac 1 2$ such that an…
In the pairwise weighted spanner problem, the input consists of an $n$-vertex-directed graph, where each edge is assigned a cost and a length. Given $k$ vertex pairs and a distance constraint for each pair, the goal is to find a…
$k$-center is one of the most popular clustering models. While it admits a simple 2-approximation in polynomial time in general metrics, the Euclidean version is NP-hard to approximate within a factor of 1.93, even in the plane, if one…
Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…
Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work,…
We consider the problem of scheduling jobs on unrelated machines so as to minimize the sum of weighted completion times. Our main result is a $(3/2-c)$-approximation algorithm for some fixed $c>0$, improving upon the long-standing bound of…
We consider the weighted completion time minimization problem for capacitated parallel machines, which is a fundamental problem in modern cloud computing environments. We study settings in which the processed jobs may have varying duration,…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
The paper describes clustering problems from the combinatorial viewpoint. A brief systemic survey is presented including the following: (i) basic clustering problems (e.g., classification, clustering, sorting, clustering with an order over…