Related papers: Partitioning Items Into Mutually Exclusive Groups

Clustering is an unsupervised machine learning task that consists of identifying groups of similar objects. It has numerous applications and is increasingly used in fairness-sensitive domains where objects represent individuals, such as…

The multiple knapsack problem with grouped items aims to maximize rewards by assigning groups of items among multiple knapsacks, considering knapsack capacities. Either all items in a group are assigned or none at all. We propose algorithms…

We introduce a novel criterion in clustering that seeks clusters with limited range of values associated with each cluster's elements. In clustering or classification the objective is to partition a set of objects into subsets, called…

The Bin Packing Problem involves efficiently packing items into a limited number of bins without exceeding their capacity. In this paper, we try to answer a specific question in this field. Mathematically the combinatorial optimization…

A scalable graphical method is presented for selecting, and partitioning datasets for the training phase of a classification task. For the heuristic, a clustering algorithm is required to get its computation cost in a reasonable proportion…

Clustering is a fundamental technique in data analysis and machine learning, used to group similar data points together. Among various clustering methods, the Minimum Sum-of-Squares Clustering (MSSC) is one of the most widely used. MSSC…

Clustering is an unsupervised technique of Data Mining. It means grouping similar objects together and separating the dissimilar ones. Each object in the data set is assigned a class label in the clustering process using a distance measure.…

Team assembly is a problem that demands trade-offs between multiple fairness criteria and computational optimization. We focus on four criteria: (i) fair distribution of workloads within the team, (ii) fair distribution of skills and…

In group testing, the goal is to identify a subset of defective items within a larger set of items based on tests whose outcomes indicate whether at least one defective item is present. This problem is relevant in areas such as medical…

We consider the problem of grouping items into clusters based on few random pairwise comparisons between the items. We introduce three closely related algorithms for this task: a belief propagation algorithm approximating the Bayes optimal…

We examine an important combinatorial challenge in clearing clutter using a mobile robot equipped with a manipulator, seeking to compute an optimal object removal sequence for minimizing the task completion time, assuming that each object…

The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…

Cluster analysis requires many decisions: the clustering method and the implied reference model, the number of clusters and, often, several hyper-parameters and algorithms' tunings. In practice, one produces several partitions, and a final…

One important tool is the optimal clustering of data into useful categories. Dividing similar objects into a smaller number of clusters is of importance in many applications. These include search engines, monitoring of academic performance,…

Clustering consists of partitioning data objects into subsets called clusters according to some similarity criteria. This paper addresses a generalization called quasi-clustering that allows overlapping of clusters, and which we link to…

We study the problem of clustering a set of items based on bandit feedback. Each of the $n$ items is characterized by a feature vector, with a possibly large dimension $d$. The items are partitioned into two unknown groups such that items…

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…

We consider the problem of assigning items to platforms in the presence of group fairness constraints. In the input, each item belongs to certain categories, called classes in this paper. Each platform specifies the group fairness…

The article proposes a heuristic approximation approach to the bin packing problem under multiple objectives. In addition to the traditional objective of minimizing the number of bins, the heterogeneousness of the elements in each bin is…

The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…