Related papers: Tractable Graph Structures in EFX Orientation
We explore the fair distribution of a set of $m$ indivisible chores among $n$ agents, where each agent's costs are evaluated using a monotone cost function. Our focus lies on two fairness criteria: envy-freeness up to any item (EFX) and a…
The Seat Arrangement Problem is a problem of finding a desirable seat arrangement for given preferences of agents and a seat graph that represents a configuration of seats. In this paper, we consider decision problems of determining if an…
We study the problem of allocating a set of indivisible goods to a set of agents with additive valuation functions, aiming to achieve approximate envy-freeness up to any good ($\alpha$-EFX). The state-of-the-art results on the problem…
We study fair division of indivisible items under a variable input setting, where the set of agents or items may change over time. Starting from an arbitrary allocation, the goal is to restore envy-freeness up to one item (EF1) through item…
Orienting the edges of an undirected graph such that the resulting digraph satisfies some given constraints is a classical problem in graph theory, with multiple algorithmic applications. In particular, an $st$-orientation orients each edge…
We study the problem of allocating indivisible objects to a set of rational agents where each agent's final utility depends on the intrinsic valuation of the allocated item as well as the allocation within the agent's local neighbourhood.…
The existence of EFX allocations is a major open problem in fair division, even for additive valuations. The current state of the art is that no setting where EFX allocations are impossible is known, and EFX is known to exist for ($i$)…
We study the problem of allocating a set of indivisible chores to three agents, among whom two have additive cost functions, in a fair manner. Two fairness notions under consideration are envy-freeness up to any chore (EFX) and a relaxed…
We study a fair division problem in (multi)graphs where $n$ agents (vertices) are pairwise connected by items (edges), and each agent is only interested in its incident items. We consider how to allocate items to incident agents in an…
We consider the fair allocation of indivisible items to several agents and add a graph theoretical perspective to this classical problem. Namely, we introduce an incompatibility relation between pairs of items described in terms of a…
We study the problem of exchange when 1) agents are endowed with heterogeneous indivisible objects, and 2) there is no money. In general, no rule satisfies the three central properties Pareto-efficiency, individual rationality, and…
We study the computational complexity of finding fair allocations of indivisible goods in the setting where a social network on the agents is given. Notions of fairness in this context are "localized", that is, agents are only concerned…
We consider the fair allocation of indivisible items to several agents with additional conflict constraints. These are represented by a conflict graph where each item corresponds to a vertex of the graph and edges in the graph represent…
We study a discrete fair division problem where $n$ agents have additive valuation functions over a set of $m$ goods. We focus on the well-known $\alpha$-EFX fairness criterion, according to which the envy of an agent for another agent is…
We consider the problem of fairly allocating the vertices of a graph among $n$ agents, where the value of a bundle is determined by its cut value -- the number of edges with exactly one endpoint in the bundle. This model naturally captures…
We study the problem of fairly and efficiently allocating indivisible goods among agents with additive valuations. We focus on envy-freeness up to any good (EFX) -- an important fairness notion in fair division of indivisible goods. A…
We consider fair allocation of indivisible items under an additional constraint: there is an undirected graph describing the relationship between the items, and each agent's share must form a connected subgraph of this graph. This framework…
The NP-hard general factor problem asks, given a graph and for each vertex a list of integers, whether the graph has a spanning subgraph where each vertex has a degree that belongs to its assigned list. The problem remains NP-hard even if…
A tangle is a connected topological space constructed by gluing several copies of the unit interval $[0, 1]$. We explore which tangles guarantee envy-free allocations of connected shares for n agents, meaning that such allocations exist no…
We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…