Related papers: Complete Graph Identification in Population Protoc…
The graph identification problem consists of discovering the interactions among nodes in a network given their state/feature trajectories. This problem is challenging because the behavior of a node is coupled to all the other nodes by the…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
In this paper, we relate the problem of finding a maximum clique to the intersection number of the input graph (i.e. the minimum number of cliques needed to edge cover the graph). In particular, we consider the maximum clique problem for…
A graph is unipolar if it can be partitioned into a clique and a disjoint union of cliques, and a graph is a generalised split graph if it or its complement is unipolar. A unipolar partition of a graph can be used to find efficiently the…
This work considers the distributed computation of the one-to-one vertex correspondences between two undirected and connected graphs, which is called \textit{graph matching}, over multi-agent networks. Given two \textit{isomorphic} and…
This paper revisits the problem of multi-agent consensus from a graph signal processing perspective. Describing a consensus protocol as a graph spectrum filter, we present an effective new approach to the analysis and design of consensus…
Secure multiparty computation (MPC) on incomplete communication networks has been studied within two primary models: (1) Where a partial network is fixed a priori, and thus corruptions can occur dependent on its structure, and (2) Where…
We study the problem of deterministically exploring an undirected and initially unknown graph with $n$ vertices either by a single agent equipped with a set of pebbles, or by a set of collaborating agents. The vertices of the graph are…
Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…
For nearly two decades, population protocols have been extensively studied, yielding efficient solutions for central problems in distributed computing, including leader election, and majority computation, a predicate type in Presburger…
We consider the following problem - a group of mobile agents perform some task on a terrain modeled as a graph. In a given moment of time an adversary gets an access to the graph and positions of the agents. Shortly before adversary's…
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 population protocols, a model of distributed computing appropriate for modeling well-mixed chemical reaction networks and other physical systems where agents exchange information in pairwise interactions, but have no control over…
The population protocol model was introduced by Angluin \emph{et al.} as a model of passively mobile anonymous finite-state agents. This model computes a predicate on the multiset of their inputs via interactions by pairs. The original…
We investigate the asymptotic structure of a random perfect graph $P_n$ sampled uniformly from the perfect graphs on vertex set $\{1,\ldots,n\}$. Our approach is based on the result of Pr\"omel and Steger that almost all perfect graphs are…
An identifying code $C$ of a graph $G$ is a dominating set of $G$ such that any two distinct vertices of $G$ have distinct closed neighbourhoods within $C$. These codes have been widely studied for over two decades. We give an improvement…
In this work, we initiate the study of \emph{smoothed analysis} of population protocols. We consider a population protocol model where an adaptive adversary dictates the interactions between agents, but with probability $p$ every such…
Let $G$ be a group. The \emph{power graph} of $G$ is a graph with the vertex set $G$, having an edge between two elements whenever one is a power of the other. We characterize nilpotent groups whose power graphs have finite independence…
In this article, we study the fundamental limits in the design of fair and/or private representations achieving perfect demographic parity and/or perfect privacy through the lens of information theory. More precisely, given some useful data…
We study allocation problems without monetary transfers where agents have correlated types, i.e., hold private information about one another. Such peer information is relevant in various settings, including science funding, allocation of…