Related papers: The Complexity of Envy-Free Graph Cutting

We study the problem of partitioning a set of agents into coalitions based on the agents' additively separable preferences, which can also be viewed as a hedonic game. We apply three successively weaker solution concepts, namely…

Fair division mechanisms for indivisible goods require agent orderings to deterministically select one allocation when running the algorithm in practice. We introduce position envy-freeness up to one good (PEF1) as a fairness criterion for…

This paper addresses the problem of finding fair orientations of graphs of chores, in which each vertex corresponds to an agent, each edge corresponds to a chore, and a chore has zero marginal utility to an agent if its corresponding edge…

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…

In this article we propose a probabilistic framework in order to study the fair division of a divisible good, e.g., a cake, between n players. Our framework follows the same idea than the ''Full independence model'' used in the study of…

There is arbitrariness in optimum solutions of graph-theoretic problems that can give rise to unfairness. Incorporating fairness in such problems, however, can be done in multiple ways. For instance, fairness can be defined on an individual…

We study the problem of fairly dividing a heterogeneous resource, commonly known as cake cutting and chore division, in the presence of strategic agents. While a number of results in this setting have been established in previous works,…

In fair division of a connected graph $G = (V, E)$, each of $n$ agents receives a share of $G$'s vertex set $V$. These shares partition $V$, with each share required to induce a connected subgraph. Agents use their own valuation functions…

A matching cut is a matching that is also an edge cut. In the problem Minimum Matching Cut, we ask for a matching cut with the minimum number of edges in the matching. We investigate the differences in complexity between Minimum Matching…

We consider a one-sided matching problem where agents who are partitioned into disjoint classes and each class must receive fair treatment in a desired matching. This model, proposed by Benabbou et al. [2019], aims to address various…

When allocating indivisible resources or tasks, an envy-free allocation or equitable allocation may not exist. We present a sufficient condition and an algorithm to achieve envy-freeness and equitability when monetary transfers are allowed.…

For any particular class of graphs, algorithms for computational problems restricted to the class often rely on structural properties that depend on the specific problem at hand. This begs the question if a large set of such results can be…

We study the stable matching problem in non-bipartite graphs with incomplete but strict preference lists, where the edges have weights and the goal is to compute a stable matching of minimum or maximum weight. This problem is known to be…

Let G=(V,E) be a graph. A vertex dominates itself and all its neighbors, i.e., every vertex v in V dominates its closed neighborhood N[v]. A vertex set D in G is an efficient dominating (e.d.) set for G if for every vertex v in V, there is…

We study the computational complexity of "public goods games on networks". In this model, each vertex in a graph is an agent that needs to take a binary decision of whether to "produce a good" or not. Each agent's utility depends on the…

Perfect Matching-Cut is the problem of deciding whether a graph has a perfect matching that contains an edge-cut. We show that this problem is NP-complete for planar graphs with maximum degree four, for planar graphs with girth five, for…

We study the problem of allocating indivisible resources under the connectivity constraints of a graph $G$. This model, initially introduced by Bouveret et al. (published in IJCAI, 2017), effectively encompasses a diverse array of scenarios…

A set of divisible resources becomes available over a sequence of rounds and needs to be allocated immediately and irrevocably. Our goal is to distribute these resources to maximize fairness and efficiency. Achieving any non-trivial…

The K-way vertex cut problem} consists in, given a graph G, finding a subset of vertices of a given size, whose removal partitions G into the maximum number of connected components. This problem has many applications in several areas. It…

We study the problem of fairly allocating indivisible items and a desirable heterogeneous divisible good (i.e., cake) to agents with additive utilities. In our paper, each indivisible item can be a good that yields non-negative utilities to…