CLEMENTI , Andrea

We study parallel \emph{Load Balancing} protocols for a client-server distributed model defined as follows. There is a set $\sC$ of $n$ clients and a set $\sS$ of $n$ servers where each client has (at most) a constant number $d \geq 1$ of requests that must be assigned to some server. The client set and the server one are connected to each...

International audience

In several real Multi-Agent Systems (MAS), it has been observed that only weaker forms of metastable consensus are achieved, in which a large majority of agents agree on some opinion while other opinions continue to be supported by a (small) minority of agents. In this work, we take a step towards the investigation of metastable consensus...

Distributed Computing Column 77

Journal version of https://hal.science/hal-02487650v2.

International audience

Motivated by the \emph{Lévy foraging hypothesis} -- the premise that various animal species have adapted to follow \emph{Lévy walks} to optimize their search efficiency -- we study the parallel hitting time of Lévy walks on the infinite two-dimensional grid.We consider $k$ independent discrete-time Lévy walks, with the same exponent $\alpha...

It follows from the Marcus-Spielman-Srivastava proof of the Kadison-Singer conjecture that if $G=(V,E)$ is a $\Delta$-regular dense expander then there is an edge-induced subgraph $H=(V,E_H)$ of $G$ of constant maximum degree which is also an expander. As with other consequences of the MSS theorem, it is not clear how one would explicitly...

Given an underlying graph, we consider the following dynamics: Initially, each node locally chooses a value in {−1, 1}, uniformly at random and independently of other nodes. Then, in each consecutive round, every node updates its local value to the average of the values held by its neighbors, at the same time applying an elementary, local...

International audience

Consensus and Broadcast are two fundamental problems in distributed computing, whose solutions have several applications. Intuitively, Consensus should be no harder than Broadcast , and this can be rigorously established in several models. Can Consensus be easier than Broadcast? In models that allow noiseless communication, we prove a reduction...

In the Random Subset Sum Problem, given $n$ i.i.d. random variables $X_1, ..., X_n$, we wish to approximate any point $z \in [-1,1]$ as the sum of a suitable subset $X_{i_1(z)}, ..., X_{i_s(z)}$ of them, up to error $\varepsilon$. Despite its simple statement, this problem is of fundamental interest to both theoretical computer science and...