Related papers: Elementary solution to the fair division problem
In fair division of indivisible goods, using sequences of sincere choices (or picking sequences) is a natural way to allocate the objects. The idea is the following: at each stage, a designated agent picks one object among those that…
Ranking, and inferences based on ranking of a set of entities, are important problems in numerous contexts. This is especially true in small area statistics where there may be only a limited amount of directly observed data from each entity…
Fair allocation has been studied intensively in both economics and computer science, and fair sharing of resources has aroused renewed interest with the advent of virtualization and cloud computing. Prior work has typically focused on…
Center-based clustering (e.g., $k$-means, $k$-medians) and clustering using linear subspaces are two most popular techniques to partition real-world data into smaller clusters. However, when the data consists of sensitive demographic…
We consider the following control problem on fair allocation of indivisible goods. Given a set $I$ of items and a set of agents, each having strict linear preference over the items, we ask for a minimum subset of the items whose deletion…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
Comparing and recognizing metrics can be extraordinarily difficult because of the group of diffeomorphisms. Two metrics, that could even be the same, could look completely different in different coordinates. This is the gauge problem. The…
One of the important yet insufficiently studied subjects in fair allocation is the externality effect among agents. For a resource allocation problem, externalities imply that a bundle allocated to an agent may affect the utilities of other…
We propose a primal-dual parallel proximal splitting method for solving domain decomposition problems for partial differential equations. The problem is formulated via minimization of energy functions on the subdomains with coupling…
New variational formulations are devised for the curl--div system, and the corresponding finite element approximations are shown to converge. Curl--free and divergence--free finite elements are employed for discretizing the problem.
This paper investigates a new class of equations called measure functional differential equations with state-dependent delays. We establish the existence and uniqueness of solutions and present a discussion concerning the appropriate phase…
We study the problem of learning classifiers with a fairness constraint, with three main contributions towards the goal of quantifying the problem's inherent tradeoffs. First, we relate two existing fairness measures to cost-sensitive…
A major open question in fair allocation of indivisible items is whether there always exists an allocation of chores that is Pareto optimal (PO) and envy-free up to one item (EF1). We answer this question affirmatively for the natural class…
The paper considers fair allocation of resources that are already allocated in an unfair way. This setting requires a careful balance between the fairness considerations and the rights of the present owners. The paper presents re-division…
We study a fair resource scheduling problem, where a set of interval jobs are to be allocated to heterogeneous machines controlled by agents. Each job is associated with release time, deadline, and processing time such that it can be…
The fair division literature in economics considers how to divide resources between multiple agents such that the allocation is envy-free: each agent receives their favorite piece. Researchers have developed a variety of fair division…
When utilities are additive, we uncovered in our previous paper (Bogomolnaia et al. "Dividing Goods or Bads under Additive Utilities") many similarities but also surprising differences in the behavior of the familiar Competitive rule (with…
We design and analyze an iterative two-grid algorithm for the finite element discretizations of strongly nonlinear elliptic boundary value problems in this paper. We propose an iterative two-grid algorithm, in which a nonlinear problem is…
We study the question of existence and fast computation of fair and efficient allocations of indivisible resources among agents with additive valuations. As such allocations may not exist for arbitrary instances, we ask if they exist for…
We study some measure partition problems: Cut the same positive fraction of $d+1$ measures in $\mathbb R^d$ with a hyperplane or find a convex subset of $\mathbb R^d$ on which $d+1$ given measures have the same prescribed value. For both…