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DTSTART;TZID=Europe/Paris:20230221T100000
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DTSTAMP:20260504T000344
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SUMMARY:Séminaire Algorithmique : Mehdi Naima « Extending Brandes algorithm to improve betweenness centrality computation in temporal graphs with discrete and continuous time »
DESCRIPTION:Betweenness centrality has been a long subject of study in network science since it was introduced by Freeman in 1977. This centrality measure assesses the importance of nodes in a graph\, it has been used for example in social\, biological and research collaboration networks. Moreover\, betweenness centrality has been used in graph partitioning and community detection in the well-known Girvan-Newan algorithm.\n\nThis centrality measure is based on the enumeration of shortest paths passing through a node. A simple approach to compute betweenness centrality for all the nodes of a static graph is to use Floyd-Warshall algorithm that runs in O(n3). Brandes in 2001 published an algorithm that runs in O(nm + n2 log n) on weighted graphs\,  it is still considered one of the best theoretical results on the question.\n\nBetweenness centrality has also been extended to temporal graphs. Temporal graphs have edges that bear labels according to the time of the interactions between the nodes. Betweenness centrality has been extended to the temporal graph settings\, and the notion of paths has been extended to temporal paths. We will see that we are able to deploy Brandes algorithm to its full extent and improve the running time of recent results to O(nmT + n2Tlog(nT)). We will also discuss how Brandes algorithm can also be generalized to stream graphs which are dynamic graphs with continuous time and dynamicity on the nodes.
URL:https://www.greyc.fr/event/seminaire-algorithmique-mehdi-naima/
LOCATION:Sciences 3- S3 351
CATEGORIES:Amacc,General,Séminaire Algo
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DTSTART;TZID=Europe/Paris:20230228T100000
DTEND;TZID=Europe/Paris:20230228T120000
DTSTAMP:20260504T000344
CREATED:20230125T165233Z
LAST-MODIFIED:20230224T142635Z
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SUMMARY:Séminaire Algorithmique : « Algorithmes pour la Dimension Métrique dans les graphes dirigés » Antoine Dailly (LIMOS\, Univ. Clermont-Ferrand)
DESCRIPTION:Résumé :\nLe problème de la Dimension Métrique d’un graphe se pose de la façon suivante : on cherche un ensemble R de sommets de taille minimale tel que\, pour toute paire de sommets du graphe\, il existe un sommet de R dont les distances aux deux sommets de la paire sont distinctes. Ce problème a été principalement étudié dans les graphes non-dirigés\, et il a attiré l’attention ces dernières années\, notamment en raison de sa difficulté : il est NP-complet et son meilleur facteur d’approximation en temps polynomial est log(n)\, y compris sur des classes de graphes très restreintes. \nNous considérons ce problèmes dans les graphes dirigés et orientés (la différence est que les graphes dirigés peuvent contenir des 2-cycles\, au contraire des graphes orientés)\, pour lesquels la Dimension Métrique a été récemment étudiée. Nous montrons que le problème reste NP-dur\, même dans les graphes orientés planaires bipartis de degré maximum 6. Cependant\, nous donnons des algorithmes linéaires résolvant le problème sur les arbres dirigés (les graphes dirigés dont le graphe sous-jacent est un arbre) et les orientations de graphes unicycliques. Enfin\, nous avons un algorithme paramétré par la largeur modulaire. \n\nAbstract:\nIn graph theory\, the Metric Dimension problem is the following: we are looking for a minimum-size set R of vertices\, such that for any pair of vertices of the graph\, there is a vertex from R whose two distances to the vertices of the pair are distinct. This problem has mainly been studied on undirected graphs\, and has gained a lot of attention in recent years\, mainly because of its difficulty: it is NP-complete and has a best polynomial-time approximation factor of log(n) even on very restricted graph classes. \nWe focus our study on directed and oriented graphs (the difference is that directed graphs may contain 2-cycles\, unlike oriented graphs)\, for which the Metric Dimension has been recently studied. We prove that Metric Dimension remains NP-hard\, even on planar bipartite oriented graphs of maximum degree 6. However\, we find linear-time algorithms solving the problem on directed trees (directed graphs whose underlying graph is a tree) and on orientations of unicyclic graphs. Finally\, we give a fixed-parameter-tractable algorithm for directed graphs when parameterised by modular-width.
URL:https://www.greyc.fr/event/seminaire-algorithmique-antoine-dailly-limos-univ-clermont-ferrand/
LOCATION:Sciences 3- S3 351
CATEGORIES:Amacc,General,Séminaire Algo
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