3,541 research outputs found
Efficient computation of the Shapley value for game-theoretic network centrality
The Shapley valueâprobably the most important normative payoff division scheme in coalitional gamesâhas recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world applications (including social and organisational networks, biological networks and communication networks), its computational properties have not been widely studied. To date, the only practicable approach to compute Shapley value-based centrality has been via Monte Carlo simulations which are computationally expensive and not guaranteed to give an exact answer. Against this background, this paper presents the first study of the computational aspects of the Shapley value for network centralities. Specifically, we develop exact analytical formulae for Shapley value-based centrality in both weighted and unweighted networks and develop efficient (polynomial time) and exact algorithms based on them. We empirically evaluate these algorithms on two real-life examples (an infrastructure network representing the topology of the Western States Power Grid and a collaboration network from the field of astrophysics) and demonstrate that they deliver significant speedups over the Monte Carlo approach. Fo
Applications of Temporal Graph Metrics to Real-World Networks
Real world networks exhibit rich temporal information: friends are added and
removed over time in online social networks; the seasons dictate the
predator-prey relationship in food webs; and the propagation of a virus depends
on the network of human contacts throughout the day. Recent studies have
demonstrated that static network analysis is perhaps unsuitable in the study of
real world network since static paths ignore time order, which, in turn,
results in static shortest paths overestimating available links and
underestimating their true corresponding lengths. Temporal extensions to
centrality and efficiency metrics based on temporal shortest paths have also
been proposed. Firstly, we analyse the roles of key individuals of a corporate
network ranked according to temporal centrality within the context of a
bankruptcy scandal; secondly, we present how such temporal metrics can be used
to study the robustness of temporal networks in presence of random errors and
intelligent attacks; thirdly, we study containment schemes for mobile phone
malware which can spread via short range radio, similar to biological viruses;
finally, we study how the temporal network structure of human interactions can
be exploited to effectively immunise human populations. Through these
applications we demonstrate that temporal metrics provide a more accurate and
effective analysis of real-world networks compared to their static
counterparts.Comment: 25 page
Fast Shortest Path Distance Estimation in Large Networks
We study the problem of preprocessing a large graph so that point-to-point shortest-path queries can be answered very fast. Computing shortest paths is a well studied problem, but exact algorithms do not scale to huge graphs encountered on the web, social networks, and other applications.
In this paper we focus on approximate methods for distance estimation, in particular using landmark-based distance indexing. This approach involves selecting a subset of nodes as landmarks and computing (offline) the distances from each node in the graph to those landmarks. At runtime, when the distance between a pair of nodes is needed, we can estimate it quickly by combining the precomputed distances of the two nodes to the landmarks.
We prove that selecting the optimal set of landmarks is an NP-hard problem, and thus heuristic solutions need to be employed. Given a budget of memory for the index, which translates directly into a budget of landmarks, different landmark selection strategies can yield dramatically different results in terms of accuracy. A number of simple methods that scale well to large graphs are therefore developed and experimentally compared. The simplest methods choose central nodes of the graph, while the more elaborate ones select central nodes that are also far away from one another. The efficiency of the suggested techniques is tested experimentally using five different real world graphs with millions of edges; for a given accuracy, they require as much as 250 times less space than the current approach in the literature which considers selecting landmarks at random.
Finally, we study applications of our method in two problems arising naturally in large-scale networks, namely, social search and community detection.Yahoo! Research (internship
Scalable Algorithms for the Analysis of Massive Networks
Die Netzwerkanalyse zielt darauf ab, nicht-triviale Erkenntnisse aus vernetzten Daten zu gewinnen. Beispiele fĂŒr diese Erkenntnisse sind die Wichtigkeit einer EntitĂ€t im VerhĂ€ltnis zu anderen nach bestimmten Kriterien oder das Finden des am besten geeigneten Partners fĂŒr jeden Teilnehmer eines Netzwerks - bekannt als Maximum Weighted Matching (MWM).
Da der Begriff der Wichtigkeit an die zu betrachtende Anwendung gebunden ist, wurden zahlreiche ZentralitĂ€tsmaĂe eingefĂŒhrt. Diese MaĂe stammen hierbei aus Jahrzehnten, in denen die Rechenleistung sehr begrenzt war und die Netzwerke im Vergleich zu heute viel kleiner waren. Heute sind massive Netzwerke mit Millionen von Kanten allgegenwĂ€rtig und eine triviale Berechnung von ZentralitĂ€tsmaĂen ist oft zu zeitaufwĂ€ndig. DarĂŒber hinaus ist die Suche nach der Gruppe von k Knoten mit hoher ZentralitĂ€t eine noch kostspieligere Aufgabe. Skalierbare Algorithmen zur Identifizierung hochzentraler (Gruppen von) Knoten in groĂen Graphen sind von groĂer Bedeutung fĂŒr eine umfassende Netzwerkanalyse.
Heutigen Netzwerke verĂ€ndern sich zusĂ€tzlich im zeitlichen Verlauf und die effiziente Aktualisierung der Ergebnisse nach einer Ănderung ist eine Herausforderung. Effiziente dynamische Algorithmen sind daher ein weiterer wesentlicher Bestandteil moderner Analyse-Pipelines.
Hauptziel dieser Arbeit ist es, skalierbare algorithmische Lösungen fĂŒr die zwei oben genannten Probleme zu finden. Die meisten unserer Algorithmen benötigen Sekunden bis einige Minuten, um diese Aufgaben in realen Netzwerken mit bis zu Hunderten Millionen von Kanten zu lösen, was eine deutliche Verbesserung gegenĂŒber dem Stand der Technik darstellt. AuĂerdem erweitern wir einen modernen Algorithmus fĂŒr MWM auf dynamische Graphen. Experimente zeigen, dass unser dynamischer MWM-Algorithmus Aktualisierungen in Graphen mit Milliarden von Kanten in Millisekunden bewĂ€ltigt.Network analysis aims to unveil non-trivial insights from networked data by studying relationship patterns between the entities of a network. Among these insights, a popular one is to quantify the importance of an entity with respect to the others according to some criteria. Another one is to find the most suitable matching partner for each participant of a network knowing the pairwise preferences of the participants to be matched with each other - known as Maximum Weighted Matching (MWM).
Since the notion of importance is tied to the application under consideration, numerous centrality measures have been introduced. Many of these measures, however, were conceived in a time when computing power was very limited and networks were much smaller compared to today's, and thus scalability to large datasets was not considered. Today, massive networks with millions of edges are ubiquitous, and a complete exact computation for traditional centrality measures are often too time-consuming. This issue is amplified if our objective is to find the group of k vertices that is the most central as a group. Scalable algorithms to identify highly central (groups of) vertices on massive graphs are thus of pivotal importance for large-scale network analysis.
In addition to their size, today's networks often evolve over time, which poses the challenge of efficiently updating results after a change occurs. Hence, efficient dynamic algorithms are essential for modern network analysis pipelines.
In this work, we propose scalable algorithms for identifying important vertices in a network, and for efficiently updating them in evolving networks. In real-world graphs with hundreds of millions of edges, most of our algorithms require seconds to a few minutes to perform these tasks. Further, we extend a state-of-the-art algorithm for MWM to dynamic graphs. Experiments show that our dynamic MWM algorithm handles updates in graphs with billion edges in milliseconds
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