BECCHETTI , Luca

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...

Distributed Computing Column 77

Spectral techniques have proved amongst the most effective approaches to graph clustering. However, in general they require explicit computation of the main eigenvectors of a suitable matrix (usuallythe Laplacian matrix of the graph).Recent work (e.g., Becchetti et al., SODA 2017) suggests that observing the temporal evolutionof the power...

We investigate opinion dynamics in multi-agent networks when a bias toward one of two possible opinions exists; for example, reflecting a status quo vs a superior alternative. Starting with all agents sharing an initial opinion representing the status quo, the system evolves in steps. In each step, one agent selected uniformly at random adopts...

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...

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