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Disjoint homometric sets in graphs

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Unique decomposition of homogeneous languages and application to isothetic regions

Nicolas René Jean Ninin

A language is said to be homogeneous when all its words have the same length. Homogeneous languages thus form a monoid under concatenation. It becomes freely commutative under the simultaneous actions of every permutation group G(n) on the collection of ho ...

2019

Deep learning on graph for semantic segmentation of point cloud

Alexandre Thierry Robert Cherqui

This master thesis provides in-depth explanations of how deep learning and graph theory can be used together to perform pointwise classification in 3D point clouds obtained by combinations of geospatial images. That scene understanding problem arises in a ...

2018

Distributed Diffusion Adaptation Over Graph Signals

Ali H. Sayed, Jie Chen, Roula Nassif

Most works on graph signal processing assume static graph signals, which is a limitation even in comparison to traditional DSP techniques where signals are modeled as sequences that evolve over time. For broader applicability, it is necessary to develop te ...

IEEE2018

A Novel Method for Sampling Bandlimited Graph Signals

Pascal Frossard, Pinar Akyazi, Dion Eustathios Olivier Tzamarias

In this paper we propose a novel vertex based sampling method for k-bandlimited signals lying on arbitrary graphs, that has a reasonable computational complexity and results in low reconstruction error. Our goal is to find the smallest set of vertices that ...

IEEE COMPUTER SOC2018

Graph-based Methods for Visualization and Clustering

Johann Paratte

The amount of data that we produce and consume is larger than it has been at any point in the history of mankind, and it keeps growing exponentially. All this information, gathered in overwhelming volumes, often comes with two problematic characteristics: ...

EPFL2017

Scaling a Reliable Distributed System

Alexandre David Olivier Maurer

We consider the problem of reliably connecting an arbitrarily large set of computers (nodes) with communication channels. Reliability means here the ability, for any two nodes, to remain connected (i.e., their ability to communicate) with probability at le ...

LPD EPFL2016

Independence number of generalized Petersen graphs

Javad Ebrahimi Boroojeni

Determining the size of a maximum independent set of a graph G, denoted by alpha(G), is an NP-hard problem. Therefore many attempts are made to find upper and lower bounds, or exact values of alpha(G) for special classes of graphs. This paper is aimed towa ...

Charles Babbage Res Ctr2016

On random subgraphs of Kneser and Schrijver graphs

Andrei Kupavskii

A Kneser graph KG(n,k) is a graph whose vertices are in oneto-one correspondence with k -element subsets of [n], with two vertices connected if and only if the corresponding sets do not intersect. A famous result due to Lowisz states that the chromatic num ...

Academic Press Inc Elsevier Science2016

On the energy benefit of compute-and-forward for multiple unicasts

Michael Christoph Gastpar, Jasper Goseling

Compute-and-forward (CF) is a technique which exploits broadcast and superposition in wireless networks. In this paper, the CF energy benefit is studied for networks with unicast sessions and modeled by connected graphs. This benefit is defined as the rati ...

Ieee2016

A Precise Threshold For Quasi-Ramsey Numbers

János Pach

We consider the variation of Ramsey numbers introduced by Erdos and Pach [J. Graph Theory, 7 (1983), pp. 137-147], where instead of seeking complete or independent sets we only seek a t-homogeneous set, a vertex subset that induces a subgraph of minimum de ...

Siam Publications2015