Related papers: Logarithmic algorithms for fair division problems

Single minded agents have strict preferences, in which a bundle is acceptable only if it meets a certain demand. Such preferences arise naturally in scenarios such as allocating computational resources among users, where the goal is to…

Machine-learned systems are in widespread use for making decisions about humans, and it is important that they are fair, i.e., not biased against individuals based on sensitive attributes. We present runtime verification of algorithmic…

Triangular factorizations are an important tool for solving integral equations and partial differential equations with hierarchical matrices ($\mathcal{H}$-matrices). Experiments show that using an $\mathcal{H}$-matrix LR factorization to…

We revisit the classic problem of fair division from a mechanism design perspective, using {\em Proportional Fairness} as a benchmark. In particular, we aim to allocate a collection of divisible items to a set of agents while incentivizing…

We study the canonical fair clustering problem where each cluster is constrained to have close to population-level representation of each group. Despite significant attention, the salient issue of having incomplete knowledge about the group…

In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing…

Proportional apportionment is the problem of assigning seats to parties according to their relative share of votes. Divisor methods are the de-facto standard solution, used in many countries. In recent literature, there are two algorithms…

We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…

An original approach to solving rather difficult probabilistic problems arising in studying the readout of random discrete fields and having no exact analytical solutions at the moment is proposed. Several algorithms for direct, iterative,…

We often add arithmetic to extend the expressiveness of query languages and study the complexity of problems such as testing query containment and finding certain answers in the framework of answering queries using views. When adding…

We consider the task of performing probabilistic inference with probabilistic logical models. Many algorithms for approximate inference with such models are based on sampling. From a logic programming perspective, sampling boils down to…

Machine learning actively impacts our everyday life in almost all endeavors and domains such as healthcare, finance, and energy. As our dependence on the machine learning increases, it is inevitable that these algorithms will be used to…

In this paper, we study the classic problem of fairly allocating indivisible items with the extra feature that the items lie on a line. Our goal is to find a fair allocation that is contiguous, meaning that the bundle of each agent forms a…

We propose an algebraic geometric approach for studying rational solutions of first-order algebraic ordinary difference equations. For an autonomous first-order algebraic ordinary difference equations, we give an upper bound for the degrees…

Metric search commonly involves finding objects similar to a given sample object. We explore a generalization, where the desired result is a fair tradeoff between multiple query objects. This builds on previous results on complex queries,…

We initiate the study of fair classifiers that are robust to perturbations in the training distribution. Despite recent progress, the literature on fairness has largely ignored the design of fair and robust classifiers. In this work, we…

In this paper we discuss the basic problems of algorithmic algebraic number theory. The emphasis is on aspects that are of interest from a purely mathematical point of view, and practical issues are largely disregarded. We describe what has…

Testing machine learning software for ethical bias has become a pressing current concern. In response, recent research has proposed a plethora of new fairness metrics, for example, the dozens of fairness metrics in the IBM AIF360 toolkit.…

Diversity maximization aims to select a diverse and representative subset of items from a large dataset. It is a fundamental optimization task that finds applications in data summarization, feature selection, web search, recommender…

We provide a technique to obtain explicit bounds for problems that can be reduced to linear forms in three complex logarithms of algebraic numbers. This technique can produce bounds significantly better than general results on lower bounds…