On the Tree Conjecture for the Network Creation Game

We analyze the structure of equilibria and the price of anarchy in the family of network creation games considered extensively in the past few years, which attempt to unify the network design and network routing problems by modeling both creation and usage costs. In general, the games are played on a host graph, where each node is a selfish independent agent (player) and each edge has a fixed link creation cost~$\alpha$. Together the agents create a network (a subgraph of the host graph) while selfishly minimizing the link creation costs plus the sum of the distances to all other players (usage cost). In this paper, we pursue two important facets of the network creation~game. First, we study extensively a natural version of the game, called the cooperative model, where nodes can collaborate and share the cost of creating any edge in the host graph. We prove the first nontrivial bounds in this model, establishing that the price of anarchy is polylogarithmic in $n$ for all values of~$\alpha$ in complete host graphs. This bound is the first result of this type for any version of the network creation game; most previous general upper bounds are polynomial in~$n$. Interestingly, we also show that equilibrium graphs have polylogarithmic diameter for the most natural range of~$\alpha$ (at most $n \mathop{\rm polylg}\nolimits n$). Second, we study the impact of the natural assumption that the host graph is a general graph, not necessarily complete. This model is a simple example of nonuniform creation costs among the edges (effectively allowing weights of $\alpha$ and~$\infty$). We prove the first assemblage of upper and lower bounds for this context, establishing nontrivial tight bounds for many ranges of~$\alpha$, for both the unilateral and cooperative versions of network creation. In particular, we establish polynomial lower bounds for both versions and many ranges of~$\alpha$, even for this simple nonuniform cost model, which sharply contrasts the conjectured constant bounds for these games in complete (uniform) graphs.

Network Creation Games(NCGs) model the creation of decentralized communication networks like the Internet. In such games strategic agents corresponding to network nodes selfishly decide with whom to connect to optimize some objective function. Past research intensively analyzed models where the agents strive for a central position in the network. This models agents optimizing the network for low-latency applications like VoIP. However, with today's abundance of streaming services it is important to ensure that the created network can satisfy the increased bandwidth demand. To the best of our knowledge, this natural problem of the decentralized strategic creation of networks with sufficient bandwidth has not yet been studied. We introduce Flow-Based NCGs where the selfish agents focus on bandwidth instead of latency. In essence, budget-constrained agents create network links to maximize their minimum or average network flow value to all other network nodes. Equivalently, this can also be understood as agents who create links to increase their connectivity and thus also the robustness of the network. For this novel type of NCG we prove that pure Nash equilibria exist, we give a simple algorithm for computing optimal networks, we show that the Price of Stability is 1 and we prove an (almost) tight bound of 2 on the Price of Anarchy. Last but not least, we show that our models do not admit a potential function.

We introduce and study the concept of an asymmetric swap-equilibrium for network creation games. A graph where every edge is owned by one of its endpoints is called to be in asymmetric swap-equilibrium, if no vertex v can delete its own edge {v,w} and add a new edge {v,w′} and thereby decrease the sum of distances from v to all other vertices. This equilibrium concept generalizes and unifies some of the previous equilibrium concepts for network creation games. While the structure and the quality of equilibrium networks is still not fully understood, we provide further (partial) insights for this open problem. As the two main results, we show that (1) every asymmetric swap-equilibrium has at most one (non-trivial) 2-edge-connected component, and (2) we show a logarithmic upper bound on the diameter of an asymmetric swap-equilibrium for the case that the minimum degree of the unique 2-edge-connected component is at least ne, for $\varepsilon>\frac{4\lg 3}{\lg n}$. Due to the generalizing property of asymmetric swap equilibria, these results hold for several equilibrium concepts that were previously studied. Along the way, we introduce a node-weighted version of the network creation games, which is of independent interest for further studies of network creation games.

Das erste Kapitel widmet sich einer Familie von Netzerzeugungsspielen. Netzerzeugungsspiele dienen der grobkörnigen Analyse von Netzwerken für die detailierte Daten nicht vorliegen, oder grundsätzlich nicht gewonnen werden können. Ein typisches Beispiel sind Soziale Netze. In den hier untersuchten Spielen wird das Netzwerk von den Knoten als den Spielern selbst gebildet. Paare von Knoten können Kanten zwischen sich einrichten oder abbrechen. Jedem Knoten entstehen feste Kosten für jede zum ihm inzidente Kante. Ein Knoten profitiert jedoch global vom Netzwerk. Jeder Knoten zieht einen Nutzen daraus, zu jedem anderen Knoten direkt oder indirekt verbunden zu sein. Dieser Nutzen ist abhängig von der Distanz der beiden Knoten im Netzwerk. Bisher konnten nur Spiele analysiert werden, in denen sich diese Distanz linear auf den Nutzen auswirkt. Wir können u.a. den Preis der Anarchie bei exponentiellen Nutzenfunktionen exakt auf 2 bestimmen. Dieses Ergebnis beruht auf einer graphentheoretischen Charakterisierung stabiler Zustände. Hiermit gelingt es auch zu zeigen, dass diese Prozesse zykeln können. Im zweiten Kapitel beschreiben wir einen approximativen Zulässigkeitstest für das sporadische Echtzeit-Ablaufplanungsproblem auf mehreren identischen Prozessoren. Eine Instanz diese Problems besteht aus einer potenziell unendlichen Folge von Aufträgen, die von einer festen Anzahl Prozessoren bearbeitet werden. Die Zuweisung der Aufträge auf die Prozessoren muss auf Grund des Echtzeitcharakters der Anwendung gemäß einer einfachen Politik erfolgen. Da die Anwendungen zudem sicherheits-kritisch sind, muss im Voraus sichergestellt werden, dass jeder Auftrag fristgerecht abgeschlossen wird. Angesichts der enormen Anzahl an Aufträgen (die häufig sogar als unendlich modelliert wird) muss ein Zulässigkeitstest dies anhand einer sehr kompakten, insbesondere endlichen, im sporadischen Fall unvollständigen Beschreibung der Instanz beurteilen. Unser Test entscheidet entweder, dass für eine Instanz kein zulässiger Ablaufplan existiert, oder dass die Instanz durch einen Ablaufplan, bei dem stets der Auftrag mit der nächstliegenden Frist als erster bearbeitet wird, auf annähernd doppelt so schnellen Prozessoren zuverlässig gelöst wird. Die Existenz eines solchen approximativen Zulässigkeitstest wurde seit den neunziger Jahren vermutet. Seither ist ebenfalls bekannt, dass die hier in Anspruch genommene Geschwindigkeitserhöhung die kleinst mögliche ist, da bereits die einfache Ablaufregel diese Erhöhung erforderlich macht. Der vorliegende Test ist damit der erste bestmögliche Test seiner Art für mehr als einen Prozessor. Im letzten Kapitel beschäftigen wir uns mit Robuster Optimierung. Robuste Optimierung ist ein spezieller Ansatz im Bereich der Optimierung unter Informationsdefizit. Anstelle verlässlicher Daten ist eine (im Allgemeinen unendliche) Menge von Szenarien gegeben. Ein leitendes Beispiel sind verspätungsresistente Fahrpläne. Die klassische robuste Optimierung sucht nach Lösungen, die in jedem dieser Szenarien zulässig sind. Dies führt zu unzumutbar konservative Lösungen. Klassische robuste Fahrpläne etwa weisen unverhältnismäßig große Pufferzeiten auf. Wir entwickeln dagegen den Begriff der Wiederherstellungfreundlichkeit (Recoverable Robustness). Eine wiederherstellungsfreundliche Lösung lässt sich mit geringem Aufwand in jedem anzunehmenden Szenario in eine zulässige Lösung verwandeln. Wir zeigen, dass dieser Begriff die Vorteile der klassischen Robustheit, insbesondere die Gütegarantie und die Lösbarkeit erhält, und dennoch weit weniger konservative Lösungen als der klassische Ansatz ermöglicht. Die Wiederherstellungsfreundlichkeit erlaubt zudem die Anwendung auf Praxisprobleme, die der klassischen robusten Optimierung vorenthalten sind. Eine wichtige Spezialisierung dieses Begriffs ist die robuste Netzpufferung. Dies ist ein verhältnismäßig einfach zu implementierendes, exaktes Verfahren, das in der Zwischenzeit bereits Anwendung in der Gleiszuweisung gefunden hat. Dort hat die Methode eine Reduzierung der Verspätung um ein Viertel bewirkt. Für ganzzahlige Varianten der robusten Netzpufferung beweisen wir u.a. Nicht-Approximierbarkeit. Neben den Anwendungs- und Modellierungsvorteilen eröffnet die Wiederherstellungsfreundlichkeit eine neue, polyedrische Sichtweise auf die lineare Optimierung unter Informationsdefizit. Diese Perspektive erlaubt es im Vorhinein den Bereich aussergewöhnlich großer Störungen zu bestimmen, in dem wiederherstellungsfreundliche Lösung immer noch beherrschbar bleiben. Wir führen an einer Reihe von Beispielen die Anwendung der Wiederherstellungsfreundlichkeit insbesondere bei der Planung von Verkehrssystemen vor. Im Zuge dessen bestimmen wir auch die Komplexität des Verspätungsmanagements, und modellieren einen durch die Anwendung motivierten alternativen Ansatz mit geringerer Komplexität.

Network creation games have been extensively studied, both by economists and computer scientists, due to their versatility in modeling individual-based community formation processes. These processes, in turn, are the theoretical counterpart of several economics, social, and computational applications on the Internet. In their several variants, these games model the tension of a player between the player’s two antagonistic goals: to be as close as possible to the other players and to activate a cheapest possible set of links. However, the generally adopted assumption is that players have a common and complete information about the ongoing network, which is quite unrealistic in practice. In this article, we consider a more compelling scenario in which players have only limited information about the network in whicy they are embedded. More precisely, we explore the game-theoretic and computational implications of assuming that players have a complete knowledge of the network structure only up to a given radius k , which is one of the most qualified local-knowledge models used in distributed computing. In this respect, we define a suitable equilibrium concept, and we provide a comprehensive set of upper and lower bounds to the price of anarchy for the entire range of values of k and for the two classic variants of the game, namely, those in which a player’s cost—besides the activation cost of the owned links—depends on the maximum/sum of all distances to the other nodes in the network, respectively. These bounds are assessed through an extensive set of experiments.

Decision-support tools are fundamental to planning road and highway infrastructure maintenance, guiding treatment interventions and their timing. Despite the development of numerous complex decision-support tools, public sector agencies frequently hesitate to adopt them. This paper presents a metamodel framework designed to bridge this gap by matching transportation asset management decision-support tools to specific decision-making contexts or scenarios, thereby promoting use of the most appropriate tools. The framework uses machine learning methods to characterise scenarios and select the most suitable model. The framework is applied to three distinct decision-support tools to determine maintenance policies for pavements and bridges: a comprehensive tool that minimises total costs (agency, user, and disruption) over a planning horizon using Monte Carlo simulation (in which random sampling is used to represent different condition states) and network equilibrium, a simplified fixed policy tool, and a tool of intermediate complexity. Trained and validated using pseudo-data from 400 scenarios across 10 simulated networks, and further tested on a realistic network, the metamodel classifier accurately predicts the most preferred decision-support tool for previously unseen scenarios.

Network simulation is used widely in network research to test new protocols, modifications to existing protocols and new ideas. The tool used in many cases is ns-2. The nature of the ns-2 protocols means that they are often based on theoretical models that might not behave in the same way as real networks. This paper presents the network simulation cradle which allows real world network stacks to be used in a wrapper that allows the stacks protocols to be used in the ns-2 network simulator. The network stacks from the open source operating systems Linux, FreeBSD and OpenBSD are included in the simulation cradle as well as a stack designed for embedded systems, 1wIP. Our results show that ns-2's TCP implementations do not match observed behaviour from real machines in some respects and using the network simulation cradle produces results closer to real world network stacks.

For about two decades, the research topic of Complex Networks has been presented ubiquitously. As a simple and effective framework to express agents and their relationships, several fields of study, from Physics to Sociology, have taken advantage of the powerful representation provided by complex networks. A particular feature inherited by almost any real world network is the presence of densely connected groups of vertices, named modules, clusters or communities. The majority of the proposed techniques does not take advantage of specific features commonly encountered on real networks, such as the power law distribution of vertices' degree (presence of hubs) and its dynamic nature, i.e. vertices, edges and communities normally does not persist invariant regarding to time. Aiming to take into account these two important features, an another ubiquitous phenomenon is applied on detecting communities: synchronization, expressed by coupled Kuramoto oscillators. Here, we extend the Kuramoto's model by introducing a negative coupling between hubs in the network. Moreover, two adjacency lists are used to represent, efficiently, the network structure. Tests have been performed in real network benchmarks, with consistent results achieved.

The k-core of a graph is the largest subgraph in which every vertex is connected to at least k other vertices within the subgraph. Core decomposition finds the k-core of the graph for every possible k. Past studies have shown important applications of core decomposition such as in the study of the properties of large networks (e.g., sustainability, connectivity, centrality, etc.), for solving NP-hard problems efficiently in real networks (e.g., maximum clique finding, densest subgraph approximation, etc.), and for large-scale network fingerprinting and visualization. The k-core is a well accepted concept partly because there exists a simple and efficient algorithm for core decomposition, by recursively removing the lowest degree vertices and their incident edges. However, this algorithm requires random access to the graph and hence assumes the entire graph can be kept in main memory. Nevertheless, real-world networks such as online social networks have become exceedingly large in recent years and still keep growing at a steady rate. In this paper, we propose the first external-memory algorithm for core decomposition in massive graphs. When the memory is large enough to hold the graph, our algorithm achieves comparable performance as the in-memory algorithm. When the graph is too large to be kept in the memory, our algorithm requires only O(k max ) scans of the graph, where k max is the largest core number of the graph. We demonstrate the efficiency of our algorithm on real networks with up to 52.9 million vertices and 1.65 billion edges.

O crescente número de alianças entre as organizações tem propiciado a formação de verdadeiras redes, configurando o que se chama hoje de Sociedade em Rede. Observa-se que a maior parte do valor dos produtos das empresas é produzida nestas redes e não mais isoladamente por uma única empresa. O presente artigo tem por objetivo discutir a estratégia de relacionamento entre os membros da cadeia produtiva no Brasil, com foco na aprendizagem e no compartilhamento do conhecimento, em contextos marcados pela inovação e pela formação de redes. São apresentados os resultados parciais de uma pesquisa em cadeias produtivas no Brasil, envolvendo 46 empresas. São analisados os relacionamentos das empresas com fornecedores, distribuidores, clientes e consumidores finais. Os resultados da pesquisa são comparados com um caso de sucesso de cadeia produtiva do setor automobilístico, descrito na literatura. Os resultados mostram que existe ainda um longo percurso a ser perseguido pela maioria das empresas para se inserirem na chamada Sociedade em Rede.

A key challenge in the social network community is the problem of network generation -- that is, how can we create synthetic networks that match characteristics traditionally found in most real world networks? Important characteristics that are present in social networks include a power law degree distribution, small diameter, and large amounts of clustering. However, most current network generators, such as the Chung Lu and Kronecker models, largely ignore the clustering present in a graph and focus on preserving other network statistics, such as the power law distribution. Models such as the exponential random graph model have a transitivity parameter that can capture clustering, but they are computationally difficult to learn, making scaling to large real world networks intractable. In this work, we propose an extension to the Chung Lu random graph model, the Transitive Chung Lu (TCL) model, which incorporates the notion transitive edges. Specifically, it combines the standard Chung Lu model with edges that are formed through transitive closure (e.g., by connecting a 'friend of a friend'). We prove TCL's expected degree distribution is equal to the degree distribution of the original input graph, while still providing the ability to capture the clustering in the network. The single parameter required by our model can be learned in seconds on graphs with millions of edges, networks can be generated in time that is linear in the number of edges. We demonstrate the performance of TCL on four real-world social networks, including an email dataset with hundreds of thousands of nodes and millions of edges, showing TCL generates graphs that match the degree distribution, clustering coefficients and hop plots of the original networks.

We initiate the study of game dynamics in the Sum Basic Network Creation Game, which was recently introduced by Alon et al.[SPAA’10]. In this game players are associated to vertices in a graph and are allowed to “swap” edges, that is to remove an incident edge and insert a new incident edge. By performing such moves, every player tries to minimize her connection cost, which is the sum of distances to all other vertices. When played on a tree, we prove that this game admits an ordinal potential function, which implies guaranteed convergence to a pure Nash Equilibrium. We show a cubic upper bound on the number of steps needed for any improving response dynamic to converge to a stable tree and propose and analyse a best response dynamic, where the players having the highest cost are allowed to move. For this dynamic we show an almost tight linear upper bound for the convergence speed. Furthermore, we contrast these positive results by showing that, when played on general graphs, this game allows best response cycles. This implies that there cannot exist an ordinal potential function and that fundamentally different techniques are required for analysing this case. For computing a best response we show a similar contrast: On the one hand we give a linear-time algorithm for computing a best response on trees even if players are allowed to swap multiple edges at a time. On the other hand we prove that this task is NP-hard even on simple general graphs, if more than one edge can be swapped at a time. The latter addresses a proposal by Alon et al..

In this paper, we introduce a measure to analyse the structural robustness of complex networks, which is specifically applicable in scenarios of targeted, sustained attacks. The measure is based on the changing size of the largest component as the network goes through disintegration. We argue that the measure can be used to quantify and compare the effectiveness of various attack strategies. Applying this measure, we confirm the result that scale-free networks are comparatively less vulnerable to random attacks and more vulnerable to targeted attacks. Then we analyse the robustness of a range of real world networks, and show that most real world networks are least robust to attacks based on betweenness of nodes. We also show that the robustness values of some networks are more sensitive to the attack strategy as compared to others. Furthermore, robustness coefficient computed using two centrality measures may be similar, even when the computational complexities of calculating these centrality measures may be different. Given this disparity, the robustness coefficient introduced potentially plays a key role in choosing attack and defence strategies for real world networks. While the measure is applicable to all types of complex networks, we clearly demonstrate its relevance to social network analysis.

Detecting the community structure exhibited by real networks is a crucial step toward an understanding of complex systems beyond the local organization of their constituents. Many algorithms proposed so far, especially the group of methods in the k-means formulation, can lead to a high degree of efficiency and accuracy. Here we test three k-means methods, based on optimal prediction, diffusion distance and dissimilarity index, respectively, on two artificial networks, including the widely known ad hoc network with same community size and a recently introduced LFR benchmark graphs with heterogeneous distributions of degree and community size. All of them display an excellent performance, with the additional advantage of low computational complexity, which enables the analysis of large systems. Moreover, successful applications to several real world networks confirm the capability of the methods.

Since community structure is an important feature of complex network, the study of community detection has attracted more and more attention in recent years. Despite most researchers focus on identifying disjoint communities, communities in many real networks often overlap. In this paper, we proposed a novel MCLC algorithm to discover overlapping communities, which using random walk on the line graph and attraction intensity. Unlike traditional random walk starting from a node, our random walk starts from a link. First we transform an undirected network graph to a weighted line graph, and then random walks on this line graph can be associated with a Markov chain. By calculating the transition probability of the Markov chain, we obtain the similarity between link pairs. Next the links can be clustered into “link communities” by a linkage method, and these nodes between link communities can be overlapping nodes. When converting the “link communities” into the “node communities”, we make a definition of attraction intensity to control the overlapping size. Finally the detected communities are permitted overlapped. Experiments on synthetic networks and some real world networks validate the effectiveness and efficiency of the proposed algorithm. Comparing overlapping modularity Q o v with other related algorithms, the results of this algorithm are satisfactory.