Related papers: Online $k$-Median with Consistent Clusters
This thesis aims to invent new approaches for making inferences with the k-means algorithm. k-means is an iterative clustering algorithm that randomly assigns k centroids, then assigns data points to the nearest centroid, and updates…
In many problems, the inputs arrive over time, and must be dealt with irrevocably when they arrive. Such problems are online problems. A common method of solving online problems is to first solve the corresponding linear program, and then…
In metric $k$-clustering, we are given as input a set of $n$ points in a general metric space, and we have to pick $k$ centers and cluster the input points around these chosen centers, so as to minimize an appropriate objective function. In…
We study the $b$-matching problem in bipartite graphs $G=(S,R,E)$. Each vertex $s\in S$ is a server with individual capacity $b_s$. The vertices $r\in R$ are requests that arrive online and must be assigned instantly to an eligible server.…
Individual fairness guarantees are often desirable properties to have, but they become hard to formalize when the dataset contains outliers. Here, we investigate the problem of developing an individually fair $k$-means clustering algorithm…
Clustering is a classic topic in optimization with $k$-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best known algorithm for $k$-means with a provable guarantee is a simple…
In the online matching on the line problem, the task is to match a set of requests $R$ online to a given set of servers $S$. The distance metric between any two points in $R\,\cup\, S$ is a line metric and the objective for the online…
Model selection is a major challenge in non-parametric clustering. There is no universally admitted way to evaluate clustering results for the obvious reason that no ground truth is available. The difficulty to find a universal evaluation…
Clustering is a fundamental unsupervised learning problem where a dataset is partitioned into clusters that consist of nearby points in a metric space. A recent variant, fair clustering, associates a color with each point representing its…
In this paper, we study the Min-cost Perfect $k$-way Matching with Delays ($k$-MPMD), recently introduced by Melnyk et al. In the problem, $m$ requests arrive one-by-one over time in a metric space. At any time, we can irrevocably make a…
Clustering is one of the most fundamental problems in unsupervised learning with a large number of applications. However, classical clustering algorithms assume that the data is static, thus failing to capture many real-world applications…
We study the classic $k$-means/median clustering, which are fundamental problems in unsupervised learning, in the setting where data are partitioned across multiple sites, and where we are allowed to discard a small portion of the data by…
In scientific computing, it is common that a mathematical expression can be computed by many different algorithms (sometimes over hundreds), each identifying a specific sequence of library calls. Although mathematically equivalent, those…
We study a fundamental online job admission problem where jobs with deadlines arrive online over time at their release dates, and the task is to determine a preemptive single-server schedule which maximizes the number of jobs that complete…
Online caching is among the most fundamental and well-studied problems in the area of online algorithms. Innovative algorithmic ideas and analysis -- including potential functions and primal-dual techniques -- give insight into this…
Machine learning algorithms are designed to make accurate predictions of the future based on existing data, while online algorithms seek to bound some performance measure (typically the competitive ratio) without knowledge of the future.…
The problem of estimating the number of clusters (say k) is one of the major challenges for the partitional clustering. This paper proposes an algorithm named k-SCC to estimate the optimal k in categorical data clustering. For the…
We study online competitive algorithms for the \emph{line chasing problem} in Euclidean spaces $\reals^d$, where the input consists of an initial point $P_0$ and a sequence of lines $X_1,X_2,...,X_m$, revealed one at a time. At each step…
The weighted $k$-server is a variant of the $k$-server problem, where the cost of moving a server is the server's weight times the distance through which it moves. The problem is famous for its intriguing properties and for evading standard…
We consider a fundamental online scheduling problem in which jobs with processing times and deadlines arrive online over time at their release dates. The task is to determine a feasible preemptive schedule on a single or multiple possibly…