Notes on sufficient conditions for a graph to be Hamiltonian

The first part of this paper deals with an extension of Dirac's Theorem to directed graphs. It is related to a result often referred to as the Ghouila-Houri Theorem. Here we show that the requirement of being strongly connected in the hypothesis of the Ghouila-Houri Theorem is redundant. The Second part of the paper shows that a condition on the number of edges for a graph to be hamiltonian implies Ore's condition on the degrees of the vertices.

Network construction and graph theoretical analysis of functional language networks in pediatric epilepsy

This dissertation introduces a new approach for assessing the effects of pediatric epilepsy on the language connectome. Two novel data-driven network construction approaches are presented. These methods rely on connecting different brain regions using either extent or intensity of language related activations as identified by independent component analysis of fMRI data. An auditory description decision task (ADDT) paradigm was used to activate the language network for 29 patients and 30 controls recruited from three major pediatric hospitals. Empirical evaluations illustrated that pediatric epilepsy can cause, or is associated with, a network efficiency reduction. Patients showed a propensity to inefficiently employ the whole brain network to perform the ADDT language task; on the contrary, controls seemed to efficiently use smaller segregated network components to achieve the same task. To explain the causes of the decreased efficiency, graph theoretical analysis was carried out. The analysis revealed no substantial global network feature differences between the patient and control groups. It also showed that for both subject groups the language network exhibited small-world characteristics; however, the patient's extent of activation network showed a tendency towards more random networks. It was also shown that the intensity of activation network displayed ipsilateral hub reorganization on the local level. The left hemispheric hubs displayed greater centrality values for patients, whereas the right hemispheric hubs displayed greater centrality values for controls. This hub hemispheric disparity was not correlated with a right atypical language laterality found in six patients. Finally it was shown that a multi-level unsupervised clustering scheme based on self-organizing maps, a type of artificial neural network, and k-means was able to fairly and blindly separate the subjects into their respective patient or control groups. The clustering was initiated using the local nodal centrality measurements only. Compared to the extent of activation network, the intensity of activation network clustering demonstrated better precision. This outcome supports the assertion that the local centrality differences presented by the intensity of activation network can be associated with focal epilepsy.^

Intracranial Volume Estimation and Graph Theoretical Analysis of Brain Functional Connectivity Networks

Understanding pathways of neurological disorders requires extensive research on both functional and structural characteristics of the brain. This dissertation introduced two interrelated research endeavors, describing (1) a novel integrated approach for constructing functional connectivity networks (FCNs) of brain using non-invasive scalp EEG recordings; and (2) a decision aid for estimating intracranial volume (ICV). The approach in (1) was developed to study the alterations of networks in patients with pediatric epilepsy. Results demonstrated the existence of statistically significant (p

Opportunistic Contact Graph Routing

L'ambiente di questa tesi è quello del Delay and Disruption Tolerant Networks (DTN), un'architettura di rete di telecomunicazioni avente come obiettivo le comunicazioni tra nodi di reti dette “challenged”, le quali devono affrontare problemi come tempi di propagazione elevati, alto tasso di errore e periodi di perdita delle connessioni. Il Bunde layer, un nuovo livello inserito tra trasporto e applicazione nell’architettura ISO/OSI, ed il protocollo ad esso associato, il Bundle Protocol (BP), sono stati progettati per rendere possibili le comunicazioni in queste reti. A volte fra la ricezione e l’invio può trascorrere un lungo periodo di tempo, a causa della indisponibilità del collegamento successivo; in questo periodo il bundle resta memorizzato in un database locale. Esistono varie implementazioni dell'architettura DTN come DTN2, implementazione di riferimento, e ION (Interplanetary Overlay Network), sviluppata da NASA JPL, per utilizzo in applicazioni spaziali; in esse i contatti tra i nodi sono deterministici, a differenza delle reti terrestri nelle quali i contatti sono generalmente opportunistici (non noti a priori). Per questo motivo all’interno di ION è presente un algoritmo di routing, detto CGR (Contact Graph Routing), progettato per operare in ambienti con connettività deterministica. È in fase di ricerca un algoritmo che opera in ambienti non deterministici, OCGR (Opportunistic Contact Graph Routing), che estende CGR. L’obiettivo di questa tesi è quello di fornire una descrizione dettagliata del funzionamento di OCGR, partendo necessariamente da CGR sul quale è basato, eseguire dei test preliminari, richiesti da NASA JPL, ed analizzarne i risultati per verificare la possibilità di utilizzo e miglioramento dell’algoritmo. Sarà inoltre descritto l’ambiente DTN e i principali algoritmi di routing per ambienti opportunistici. Nella parte conclusiva sarà presentato il simulatore DTN “The ONE” e l’integrazione di CGR e OCGR al suo interno.

Women holding a "Cut back the Pentagon" sign at an ERA demonstration

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A survey of graph and subgraph isomorphism problems

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Algorithme de branch-and-price-and-cut pour le problème de conception de réseaux avec coûts fixes, capacités et un seul produit

De nombreux problèmes liés aux domaines du transport, des télécommunications et de la logistique peuvent être modélisés comme des problèmes de conception de réseaux. Le problème classique consiste à transporter un flot (données, personnes, produits, etc.) sur un réseau sous un certain nombre de contraintes dans le but de satisfaire la demande, tout en minimisant les coûts. Dans ce mémoire, on se propose d'étudier le problème de conception de réseaux avec coûts fixes, capacités et un seul produit, qu'on transforme en un problème équivalent à plusieurs produits de façon à améliorer la valeur de la borne inférieure provenant de la relaxation continue du modèle. La méthode que nous présentons pour la résolution de ce problème est une méthode exacte de branch-and-price-and-cut avec une condition d'arrêt, dans laquelle nous exploitons à la fois la méthode de génération de colonnes, la méthode de génération de coupes et l'algorithme de branch-and-bound. Ces méthodes figurent parmi les techniques les plus utilisées en programmation linéaire en nombres entiers. Nous testons notre méthode sur deux groupes d'instances de tailles différentes (gran-des et très grandes), et nous la comparons avec les résultats donnés par CPLEX, un des meilleurs logiciels permettant de résoudre des problèmes d'optimisation mathématique, ainsi qu’avec une méthode de branch-and-cut. Il s'est avéré que notre méthode est prometteuse et peut donner de bons résultats, en particulier pour les instances de très grandes tailles.

A survey of graph and subgraph isomorphism problems

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

A Scalable General Purpose System for Large-Scale Graph Processing

Graph analytics is an important and computationally demanding class of data analytics. It is essential to balance scalability, ease-of-use and high performance in large scale graph analytics. As such, it is necessary to hide the complexity of parallelism, data distribution and memory locality behind an abstract interface. The aim of this work is to build a scalable graph analytics framework that does not demand significant parallel programming experience based on NUMA-awareness.
The realization of such a system faces two key problems:
(i)~how to develop a scale-free parallel programming framework that scales efficiently across NUMA domains; (ii)~how to efficiently apply graph partitioning in order to create separate and largely independent work items that can be distributed among threads.

Graph analysis of verbal fluency test discriminate between patients with Alzheimer’s disease, Mild Cognitive Impairment and normal elderly controls

Verbal fluency is the ability to produce a satisfying sequence of spoken words during a given time interval. The core of verbal fluency lies in the capacity to manage the executive aspects of language. The standard scores of the semantic verbal fluency test are broadly used in the neuropsychological assessment of the elderly, and different analytical methods are likely to extract even more information from the data generated in this test. Graph theory, a mathematical approach to analyze relations between items, represents a promising tool to understand a variety of neuropsychological states. This study reports a graph analysis of data generated by the semantic verbal fluency test by cognitively healthy elderly (NC), patients with Mild Cognitive Impairment – subtypes amnestic(aMCI) and amnestic multiple domain (a+mdMCI) - and patients with Alzheimer’s disease (AD). Sequences of words were represented as a speech graph in which every word corresponded to a node and temporal links between words were represented by directed edges. To characterize the structure of the data we calculated 13 speech graph attributes (SGAs). The individuals were compared when divided in three (NC – MCI – AD) and four (NC – aMCI – a+mdMCI – AD) groups. When the three groups were compared, significant differences were found in the standard measure of correct words produced, and three SGA: diameter, average shortest path, and network density. SGA sorted the elderly groups with good specificity and sensitivity. When the four groups were compared, the groups differed significantly in network density, except between the two MCI subtypes and NC and aMCI. The diameter of the network and the average shortest path were significantly different between the NC and AD, and between aMCI and AD. SGA sorted the elderly in their groups with good specificity and sensitivity, performing better than the standard score of the task. These findings provide support for a new methodological frame to assess the strength of semantic memory through the verbal fluency task, with potential to amplify the predictive power of this test. Graph analysis is likely to become clinically relevant in neurology and psychiatry, and may be particularly useful for the differential diagnosis of the elderly.

Multilevel mesh partitioning for optimising domain shape

Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem for mapping meshes onto parallel computers. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. To date these algorithms have been used almost exclusively to minimise the cut-edge weight in the graph with the aim of minimising the parallel communication overhead. However it has been shown that for certain classes of problem, the convergence of the underlying solution algorithm is strongly influenced by the shape or aspect ratio of the subdomains. In this paper therefore, we modify the multilevel algorithms in order to optimise a cost function based on aspect ratio. Several variants of the algorithms are tested and shown to provide excellent results.

Multilevel mesh partitioning for optimising subdomain aspect ratio

Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem for mapping meshes onto parallel computers. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. To date these algorithms have been used almost exclusively to minimise the cut-edge weight in the graph with the aim of minimising the parallel communication overhead. However it has been shown that for certain classes of problem, the convergence of the underlying solution algorithm is strongly influenced by the shape or aspect ratio of the subdomains. In this paper therefore, we modify the multilevel algorithms in order to optimise a cost function based on aspect ratio. Several variants of the algorithms are tested and shown to provide excellent results.

Multilevel mesh partitioning for aspect ratio

Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. To date these algorithms have been used almost exclusively to minimise the cut-edge weight, however it has been shown that for certain classes of solution algorithm, the convergence of the solver is strongly influenced by the subdomain aspect ratio. In this paper therefore, we modify the multilevel algorithms in order to optimise a cost function based on aspect ratio. Several variants of the algorithms are tested and shown to provide excellent results.