Related papers: Generalized Load Balancing and Clustering Problems…
In inverse optimization problems, the goal is to modify the costs in an underlying optimization problem in such a way that a given solution becomes optimal, while the difference between the new and the original cost functions, called the…
We study the problem of partitioning a set of $n$ objects in a metric space into $k$ clusters $V_1,\dots,V_k$. The quality of the clustering is measured by considering the vector of cluster costs and then minimizing some monotone symmetric…
Clustering is an unsupervised learning task that aims to partition data into a set of clusters. In many applications, these clusters correspond to real-world constructs (e.g. electoral districts) whose benefit can only be attained by groups…
We introduce a general random model of a combinatorial optimization problem with geometric structure that encapsulates both linear programming and integer linear programming. Let $Q$ be a bounded set called the feasible set, $E$ be an…
We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job…
Clustering is a well-studied unsupervised learning task that aims to partition data points into a number of clusters. In many applications, these clusters correspond to real-world constructs (e.g., electoral districts, playlists, TV…
We consider a general load balancing problem on parallel machines. Our machine environment in particular generalizes the standard models of identical machines, and the model of uniformly related machines, as well as machines with a constant…
We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for…
One of the most ubiquitous problems in optimization is that of finding all the elements of a finite set at which a function $f$ attains its minimum (or maximum). When the codomain of $f$ is equipped with a total order, it is easy to…
We present consistent algorithms for multiclass learning with complex performance metrics and constraints, where the objective and constraints are defined by arbitrary functions of the confusion matrix. This setting includes many common…
Correlation Clustering is a powerful graph partitioning model that aims to cluster items based on the notion of similarity between items. An instance of the Correlation Clustering problem consists of a graph $G$ (not necessarily complete)…
This paper considers correlation clustering on unweighted complete graphs. We give a combinatorial algorithm that returns a single clustering solution that is simultaneously $O(1)$-approximate for all $\ell_p$-norms of the disagreement…
Optimization problems often involve vector norms, which has led to extensive research on developing algorithms that can handle objectives beyond the $\ell_p$ norms. Our work introduces the concept of submodular norms, which are a versatile…
The minimum linear ordering problem (MLOP) generalizes well-known combinatorial optimization problems such as minimum linear arrangement and minimum sum set cover. MLOP seeks to minimize an aggregated cost $f(\cdot)$ due to an ordering…
Connected clustering denotes a family of constrained clustering problems in which we are given a distance metric and an undirected connectivity graph $G$ that can be completely unrelated to the metric. The aim is to partition the $n$…
Malleable scheduling is a model that captures the possibility of parallelization to expedite the completion of time-critical tasks. A malleable job can be allocated and processed simultaneously on multiple machines, occupying the same time…
In this paper, we study a number of well-known combinatorial optimization problems that fit in the following paradigm: the input is a collection of (potentially inconsistent) local relationships between the elements of a ground set (e.g.,…
We prove polynomial-time solvability of a large class of clustering problems where a weighted set of items has to be partitioned into clusters with respect to some balancing constraints. The data points are weighted with respect to…
In minimum-cost inverse optimization problems, we are given a feasible solution to an underlying optimization problem together with a linear cost function, and the goal is to modify the costs by a small deviation vector so that the input…
Timely and effective load shedding in power systems is critical for maintaining supply-demand balance and preventing cascading blackouts. To eliminate load shedding bias against specific regions in the system, optimization-based methods are…