Related papers: Generalized Load Balancing and Clustering Problems…

In many statistical linear inverse problems, one needs to recover classes of similar curves from their noisy images under an operator that does not have a bounded inverse. Problems of this kind appear in many areas of application.…

This paper presents universal algorithms for clustering problems, including the widely studied $k$-median, $k$-means, and $k$-center objectives. The input is a metric space containing all potential client locations. The algorithm must…

Many multiobjective real-world problems, such as facility location and bus routing, become more complex when optimizing the priorities of multiple stakeholders. These are often modeled using infinite classes of objectives, e.g., $L_p$ norms…

Robust optimization is concerned with constructing solutions that remain feasible also when a limited number of resources is removed from the solution. Most studies of robust combinatorial optimization to date made the assumption that every…

Min-max optimization problems, also known as saddle point problems, have attracted significant attention due to their applications in various fields, such as fair beamforming, generative adversarial networks (GANs), and adversarial…

In the load balancing problem, introduced by Graham in the 1960s (SIAM J. of Appl. Math. 1966, 1969), jobs arriving online have to be assigned to machines so to minimize an objective defined on machine loads. A long line of work has…

We revisit the simultaneous approximation model for the correlation clustering problem introduced by Davies, Moseley, and Newman[DMN24]. The objective is to find a clustering that minimizes given norms of the disagreement vector over all…

We consider fairness in submodular maximization subject to a knapsack constraint, a fundamental problem with various applications in economics, machine learning, and data mining. In the model, we are given a set of ground elements, each…

The problem of scheduling jobs on parallel machines (identical, uniform, or unrelated), under incompatibility relation modeled as a block graph, under the makespan optimality criterion, is considered in this paper. No two jobs that are in…

Clustering problems such as $k$-Median, and $k$-Means, are motivated from applications such as location planning, unsupervised learning among others. In such applications, it is important to find the clustering of points that is not…

Graph clustering problems typically aim to partition the graph nodes such that two nodes belong to the same partition set if and only if they are similar. Correlation Clustering is a graph clustering formulation which: (1) takes as input a…

Modern data centers face a key challenge of effectively serving user requests that arrive online. Such requests are inherently multi-dimensional and characterized by demand vectors over multiple resources such as processor cycles, storage…

Assigning jobs onto identical machines with the objective to minimize the maximal load is one of the most basic problems in combinatorial optimization. Motivated by product planing and data placement, we study a natural extension called…

We consider the following node-capacitated network design problem. The input is an undirected graph, set of demands, uniform node capacity and arbitrary node costs. The goal is to find a minimum node-cost subgraph that supports all demands…

Multi-task learning (MTL) aims to build general-purpose vision systems by training a single network to perform multiple tasks jointly. While promising, its potential is often hindered by "unbalanced optimization", where task interference…

Large-scale L1-regularized loss minimization problems arise in high-dimensional applications such as compressed sensing and high-dimensional supervised learning, including classification and regression problems. High-performance algorithms…

The classical center based clustering problems such as $k$-means/median/center assume that the optimal clusters satisfy the locality property that the points in the same cluster are close to each other. A number of clustering problems arise…

In this paper we study the problem of correlation clustering under fairness constraints. In the classic correlation clustering problem, we are given a complete graph where each edge is labeled positive or negative. The goal is to obtain a…

We introduce the $(p,q)$-Fair Clustering problem. In this problem, we are given a set of points $P$ and a collection of different weight functions $W$. We would like to find a clustering which minimizes the $\ell_q$-norm of the vector over…

We study fair allocation of profit (or cost) for three central problems from combinatorial optimization: Max-Flow, MST and $b$-matching. The essentially unequivocal choice of solution concept for this purpose would be the core, because of…