Related papers: Discordant voting processes on finite graphs
We present the first nearly-optimal bounds on the consensus time for the well-known synchronous consensus dynamics, specifically 3-Majority and 2-Choices, for an arbitrary number of opinions. In synchronous consensus dynamics, we consider…
We present three voting protocols with unconditional privacy and correctness, without assuming any bound on the number of corrupt participants. All protocols have polynomial complexity and require private channels and a simultaneous…
The constrained voter model describes the dynamics of opinions in a population of individuals located on a connected graph. Each agent is characterized by her opinion, where the set of opinions is represented by a finite sequence of…
A walk $W$ in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in $W$ is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity…
Discontinuous phase transitions are closely linked to tipping points, critical mass effects, and hysteresis, phenomena that have been confirmed empirically and recognized as highly important in social systems. The multistate $q$-voter…
In this paper we study the number of vertex recolorings that an algorithm needs to perform in order to maintain a proper coloring of a graph under insertion and deletion of vertices and edges. We present two algorithms that achieve…
We present a graph model for a background independent, relational approach to spacetime emergence. The general idea and the graph main features, detailed in [1], are discussed. This is a combinatorial (dynamical) metric graph, colored on…
We consider the convergence time for solving the binary consensus problem using the interval consensus algorithm proposed by B\' en\' ezit, Thiran and Vetterli (2009). In the binary consensus problem, each node initially holds one of two…
A split graph is a graph whose vertex set can be partitioned into a clique and an independent set. A connected graph $G$ is said to be $t$-admissible if admits a special spanning tree in which the distance between any two adjacent vertices…
A proper edge coloring of a graph $G$ with colors $1,2,\dots,t$ is called a \emph{cyclic interval $t$-coloring} if for each vertex $v$ of $G$ the edges incident to $v$ are colored by consecutive colors, under the condition that color $1$ is…
Colouring the vertices of a graph $G$ according to certain conditions can be considered as a random experiment and a discrete random variable $X$ can be defined as the number of vertices having a particular colour in the proper colouring of…
We consider a modified random walk which uses unvisited edges whenever possible, and makes a simple random walk otherwise. We call such a walk an edge-process. We assume there is a rule A, which tells the walk which unvisited edge to use…
The basic idea of voting protocols is that nodes query a sample of other nodes and adjust their own opinion throughout several rounds based on the proportion of the sampled opinions. In the classic model, it is assumed that all nodes have…
A chord diagram refers to a set of chords with distinct endpoints on a circle. The intersection graph of a chord diagram $\cal C$ is defined by substituting the chords of $\cal C$ with vertices and by adding edges between two vertices…
In a previous version of this document we misinterpreted the runtime of a part of the described algorithm. Indeed, the runtime is not better than the Grover-Algorithm. We therefor withdraw this work. We present a novel algorithmic approach…
Vertex Descent is a local search algorithm which forms the basis of a wide spectrum of tabu search, simulated annealing and hybrid evolutionary algorithms for graph colouring. These algorithms are usually treated as experimental and provide…
The vertex coloring problem has received a lot of attention in the context of synchronous round-based systems where, at each round, a process can send a message to all its neighbors, and receive a message from each of them. Hence, this…
Several recent results from dynamic and sublinear graph coloring are surveyed. This problem is widely studied and has motivating applications like network topology control, constraint satisfaction, and real-time resource scheduling. Graph…
A streaming algorithm is considered to be adversarially robust if it provides correct outputs with high probability even when the stream updates are chosen by an adversary who may observe and react to the past outputs of the algorithm. We…
For a simple graph G = (V, E), a coloring of vertices of G using two colors, say red and blue, is called a quasi neighborhood balanced coloring if, for every vertex of the graph, the number of red neighbors and the number of blue neighbors…