Related papers: Randomized Communication and Implicit Graph Repres…
We explore the connection between dimensionality and communication cost in distributed learning problems. Specifically we study the problem of estimating the mean $\vec{\theta}$ of an unknown $d$ dimensional gaussian distribution in the…
Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…
The congested clique model is a message-passing model of distributed computation where the underlying communication network is the complete graph of $n$ nodes. In this paper we consider the situation where the joint input to the nodes is an…
This thesis deals with applications of experimental mathematics to a number of problems. The first problem is related to random graph statistics. We consider a certain class of Galton-Watson random trees and look at the total height…
We introduce a broad class of random graph models: the generalised hypergeometric ensemble (GHypEG). This class enables to solve some long standing problems in random graph theory. First, GHypEG provides an elegant and compact formulation…
A cut of a graph can be represented in many different ways. Here we propose to represent a cut through a ``relation tree'', which is a spanning tree with signed edges. We show that this picture helps to classify the main greedy heuristics…
Consider a distributed task where the communication network is fixed but the local inputs given to the nodes of the distributed system may change over time. In this work, we explore the following question: if some of the local inputs…
The general communication tree embedding problem is the problem of mapping a set of communicating terminals, represented by a graph G, into the set of vertices of some physical network represented by a tree T. In the case where the vertices…
Establishing dense correspondence between two images is a fundamental computer vision problem, which is typically tackled by matching local feature descriptors. However, without global awareness, such local features are often insufficient…
We study statistical problems, such as planted clique, its variants, and sparse principal component analysis in the context of average-case communication complexity. Our motivation is to understand the statistical-computational trade-offs…
We study the fundamental problem of reliable interactive communication over a noisy channel. In a breakthrough sequence of papers published in 1992 and 1993, Schulman gave non-constructive proofs of the existence of general methods to…
Can we learn the differential equations governing the evolution of a temporal network? We investigate this within Random Dot Product Graphs (RDPGs), where each network snapshot is generated from latent positions evolving under unknown…
We study common randomness where two parties have access to i.i.d. samples from a known random source, and wish to generate a shared random key using limited (or no) communication with the largest possible probability of agreement. This…
We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…
Constraint Satisfaction Problem (CSP) is a fundamental algorithmic problem that appears in many areas of Computer Science. It can be equivalently stated as computing a homomorphism $\mbox{$\bR \rightarrow \bGamma$}$ between two relational…
Distributed Constraint Optimization Problems (DCOPs) are an important subclass of combinatorial optimization problems, where information and controls are distributed among multiple autonomous agents. Previously, Machine Learning (ML) has…
A new precoding-based intersession network coding (NC) scheme has recently been proposed, which applies the interference alignment technique, originally devised for wireless interference channels, to the 3-unicast problem of directed…
The Spanning Tree Congestion (STC) problem is the following NP-hard problem: given a graph $G$, construct a spanning tree $T$ of $G$ minimizing its maximum edge congestion where the congestion of an edge $e\in T$ is the number of edges $uv$…
We study distributed computation in synchronous dynamic networks where an omniscient adversary controls the unidirectional communication links. Its behavior is modeled as a sequence of directed graphs representing the active (i.e. timely)…
Unsplittable flow problems cover a wide range of telecommunication and transportation problems and their efficient resolution is key to a number of applications. In this work, we study algorithms that can scale up to large graphs and…