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We study the following synchronous process that we call repeated balls-into-bins. The process is started by assigning n balls to n bins in an arbitrary way. Then, in every subsequent round, one ball is chosen according to some fixed strategy (random, FIFO, etc) from each non-empty bin, and re-assigned to one of the n bins uniformly at random. This process… (More)

We have a set of nodes each having one color out of There is a plurality of nodes having the same color. We want to reach consensus on the plurality color.

We study a <i>Plurality Consensus</i> process in which each of <i>n</i> anonymous agents of a communication network supports an initial opinion (a colorchosen from a finite set [<i>k</i>]) and, at every time step, he can revise his color according to a random sample of neighbors.
The goal (of the agents) is to let the process converge to the <i>stable</i>… (More)

The twentieth century has seen the rise of a new type of video games targeted at a mass audience of " casual " gamers. Many of these games require the player to swap items in order to form matches of three and are collectively known as tile-matching match-three games. Among these, the most influential one is arguably Bejeweled in which the matched items… (More)

We consider the following distributed consensus problem: Each node in a complete communication network of size n initially holds an opinion, which is chosen arbitrarily from a finite set Σ. The system must converge toward a consensus state in which all, or almost all nodes, hold the same opinion. Moreover, this opinion should be valid, i.e., it should be… (More)

We present KADABRA, a new algorithm to approximate betweenness centrality in directed and undirected graphs, which significantly outperforms all previous approaches on real-world complex networks. The efficiency of the new algorithm relies on two new theoretical contribution, of independent interest. The first contribution focuses on sampling shortest… (More)

Given an underlying network, the averaging dynamics is the following distributed process: Initially , each node sets its local value to an element of {−1, 1}, uniformly at random and independently of other nodes. Then, in each consecutive round, every node updates its value to the average of its neighbors. We show that when the graph is organized into two… (More)

In the deterministic binary majority process we are given a simple graph where each node has one out of two initial opinions. In every round, each node adopts the majority opinion among its neighbors. It is known that this process always converges in O (|E|) rounds to a two-periodic state in which every node either keeps its opinion or changes it in every… (More)