Related papers: Neighborhood Stability in Assignments on Graphs
We study the fair allocation of indivisible items subject to conflict constraints. In this framework, the items are represented as the vertices of a graph, with edges corresponding to conflicts between pairs of items. Each agent is assigned…
We study the two-player communication problem of determining whether two vertices $x, y$ are nearby in a graph $G$, with the goal of determining the graph structures that allow the problem to be solved with a constant-cost randomized…
A binary state on a graph means an assignment of binary values to its vertices. For example, if one encodes a network of spiking neurons as a directed graph, then the spikes produced by the neurons at an instant of time is a binary state on…
The Graphical House Allocation problem asks: how can $n$ houses (each with a fixed non-negative value) be assigned to the vertices of an undirected graph $G$, so as to minimize the "aggregate local envy", i.e., the sum of absolute…
Many distributed learning techniques have been motivated by the increasing size of datasets and their inability to fit into main memory on a single machine. We propose an algorithm that finds the nearest neighbor in a graph locally without…
Continuous-time signals are well known for not being perfectly localized in both time and frequency domains. Conversely, a signal defined over the vertices of a graph can be perfectly localized in both vertex and frequency domains. We…
We study stable matching problems where agents have multilayer preferences: There are $\ell$ layers each consisting of one preference relation for each agent. Recently, Chen et al. [EC '18] studied such problems with strict preferences,…
We consider a basic model of a dynamical distribution network, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…
Graph Neural Networks (GNNs) show impressive performance in many practical scenarios, which can be largely attributed to their stability properties. Empirically, GNNs can scale well on large size graphs, but this is contradicted by the fact…
Exponential family Random Graph Models (ERGMs) can be viewed as expressing a probability distribution on graphs arising from the action of competing social forces that make ties more or less likely, depending on the state of the rest of the…
Uncertainty principles present an important theoretical tool in signal processing, as they provide limits on the time-frequency concentration of a signal. In many real-world applications the signal domain has a complicated irregular…
We define the following parameter of connected graphs. For a given graph $G$ we place one agent in each vertex of $G$. Every pair of agents sharing a common edge is declared to be acquainted. In each round we choose some matching of $G$…
Given a hereditary graph property $\mathcal{P}$, consider distributions of random orderings of vertices of graphs $G\in\mathcal{P}$ that are preserved under isomorphisms and under taking induced subgraphs. We show that for many properties…
The functionality of a graph $G$ is the minimum number $k$ such that in every induced subgraph of $G$ there exists a vertex whose neighbourhood is uniquely determined by the neighborhoods of at most $k$ other vertices in the subgraph. The…
We systematically evaluate the (in-)stability of state-of-the-art node embedding algorithms due to randomness, i.e., the random variation of their outcomes given identical algorithms and graphs. We apply five node embeddings…
We study the Popular Matching problem in multiple models, where the preferences of the agents in the instance may change or may be unknown/uncertain. In particular, we study an Uncertainty model, where each agent has a possible set of…
We consider a scenario in which leaders are required to recruit teams of followers. Each leader cannot recruit all followers, but interaction is constrained according to a bipartite network. The objective for each leader is to reach a state…
We study hedonic coalition formation games in which cooperation among the players is restricted by a graph structure: a subset of players can form a coalition if and only if they are connected in the given graph. We investigate the…
Graph Neural Networks (GNNs) have shown remarkable performance on graph-structured data. However, recent empirical studies suggest that GNNs are very susceptible to distribution shift. There is still significant ambiguity about why…
In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…