# Ami Paz

## Publications Authored By Ami Paz

We present the first super-linear lower bounds for natural graph problems in the CONGEST model, answering a long-standing open question. Specifically, we show that any exact computation of a minimum vertex cover or a maximum independent set requires $\Omega(n^2/\log^2{n})$ rounds in the worst case in the CONGEST model, as well as any algorithm for $\chi$-coloring a graph, where $\chi$ is the chromatic number of the graph. We further show that such strong lower bounds are not limited to NP-hard problems, by showing two simple graph problems in P which require a quadratic and near-quadratic number of rounds. Read More

We present a simple deterministic single-pass $(2+\epsilon)$-approximation algorithm for the maximum weight matching problem in the semi-streaming model. This improves upon the currently best known approximation ratio of $(3.5+\epsilon)$. Read More

This paper studies the complexity of distributed construction of purely additive spanners in the CONGEST model. We describe algorithms for building such spanners in several cases. Because of the need to simultaneously make decisions at far apart locations, the algorithms use additional mechanisms compared to their sequential counterparts. Read More

In this work, we use algebraic methods for studying distance computation and subgraph detection tasks in the congested clique model. Specifically, we adapt parallel matrix multiplication implementations to the congested clique, obtaining an $O(n^{1-2/\omega})$ round matrix multiplication algorithm, where $\omega < 2.3728639$ is the exponent of matrix multiplication. Read More

This paper gives simple distributed algorithms for the fundamental problem of computing graph distances in the Congested Clique model. One of the main components of our algorithms is fast matrix multiplication, for which we show an $O(n^{1/3})$-round algorithm when the multiplication needs to be performed over a semi-ring, and an $O(n^{0.157})$-round algorithm when the computation can be performed over a field. Read More