Related papers: An Exponential Envy-Free Cake Cutting Protocol for…
The current practice of envy-free rent division, lead by the fair allocation website Spliddit, is based on quasi-linear preferences. These preferences rule out agents' well documented financial constraints. To resolve this issue we consider…
We consider the Global Minimum Vertex-Cut problem: given an undirected vertex-weighted graph $G$, compute a minimum-weight subset of its vertices whose removal disconnects $G$. The problem is closely related to Global Minimum Edge-Cut,…
We study envy-free pricing mechanisms in matching markets with $m$ items and $n$ budget constrained buyers. Each buyer is interested in a subset of the items on sale, and she appraises at some single-value every item in her preference-set.…
A {\it good drawing} of a graph $G$ is a drawing where the edges are non-self-intersecting and each two edges have at most one point in common, which is either a common end vertex or a crossing. The {\it crossing number} of a graph $G$ is…
How many mutually non-attacking queens can be placed on a d-dimensional chessboard of size n? The n-queens problem in higher dimensions is a generalization of the well-known n-queens problem. We provide a comprehensive overview of…
In the first chapter of their classic book "Concrete Mathematics", Graham, Knuth, and Patashnik consider the maximum number of pieces that can be obtained from a pancake by making n cuts with a knife blade that is straight, or bent into a…
In this article we suggest a model of computation for the cake cutting problem. In this model the mediator can ask the same queries as in the Robertson-Webb model but he or she can only perform algebraic operations as in the Blum-Shub-Smale…
We consider the house allocation problem, where $m$ houses are to be assigned to $n$ agents so that each agent gets exactly one house. We present a polynomial-time algorithm that determines whether an envy-free assignment exists, and if so,…
We study the problem of fairly allocating a set of $m$ goods among $n$ agents in the asymptotic setting, where each item's value for each agent is drawn from an underlying joint distribution. Prior works have shown that if this distribution…
We provide theoretical insights around the cutwidth of a graph and the One-Sided Crossing Minimization (OSCM) problem. OSCM was posed in the Parameterized Algorithms and Computational Experiments Challenge 2024, where the cutwidth of the…
We propose a fixed-parameter tractable algorithm for the \textsc{Max-Cut} problem on embedded 1-planar graphs parameterized by the crossing number $k$ of the given embedding. A graph is called 1-planar if it can be drawn in the plane with…
We study fair mechanisms for the classic job scheduling problem on unrelated machines with the objective of minimizing the makespan. This problem is equivalent to minimizing the egalitarian social cost in the fair division of chores. The…
We consider a fair division setting in which $m$ indivisible items are to be allocated among $n$ agents, where the agents have additive utilities and the agents' utilities for individual items are independently sampled from a distribution.…
In the EDGE CLIQUE COVER (ECC) problem, given a graph G and an integer k, we ask whether the edges of G can be covered with k complete subgraphs of G or, equivalently, whether G admits an intersection model on k-element universe. Gramm et…
We prove essentially tight lower bounds, conditionally to the Exponential Time Hypothesis, for two fundamental but seemingly very different cutting problems on surface-embedded graphs: the Shortest Cut Graph problem and the Multiway Cut…
We consider the problem of finding a maximum size triangle-free $2$-matching in a graph $G=(V,E)$. A (simple) $2$-matching is any subset of the edges such that each vertex is incident to at most two edges from the subset. The first…
We consider allocating indivisible goods with provable fairness guarantees that are satisfied regardless of which bundle of items each agent receives. Symmetrical allocations of this type are known to exist for divisible resources, such as…
We study the classic setting of envy-free pricing, in which a single seller chooses prices for its many items, with the goal of maximizing revenue once the items are allocated. Despite the large body of work addressing such settings, most…
An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…
We study approximation algorithms for graph pricing with vertex capacities yet without the traditional envy-free constraint. Specifically, we have a set of items $V$ and a set of customers $X$ where each customer $i \in X$ has a budget…