Parallel (k)(k)-Clique Community Detection on Large-Scale Networks

The analysis of real-world complex networks has been the focus of recent research. Detecting communities helps in uncovering their structural and functional organization. Valuable insight can be obtained by analyzing the dense, overlapping, and highly interwoven k-clique communities. However, their detection is challenging due to extensive memory requirements and execution time. In this paper, we present a novel, parallel k-clique community detection method, based on an innovative technique which enables connected components of a network to be obtained from those of its subnetworks. The novel method has an unbounded, user-configurable, and input-independent maximum degree of parallelism, and hence is able to make full use of computational resources. Theoretical tight upper bounds on its worst case time and space complexities are given as well. Experiments on real-world networks such as the Internet and the World Wide Web confirmed the almost optimal use of parallelism (i.e., a linear speedup). Comparisons with other state-of-the-art k-clique community detection methods show dramatic reductions in execution time and memory footprint. An open-source implementation of the method is also made publicly available

k-clique Communities in the Internet AS-level

A signicant challenge for researchers analysing the Internet AS-level topology graph is how to interpret the global organization of the graph as the coexistence of its structural blocks (communities) associated with more highly interconnected parts. While a huge number of papers have already been published on the issue of community detection, very little attention has so far been devoted to the discovery and interpretation of Internet communities at the various levels of abstractions. We believe that by discovering and interpreting a priori these unknown building blocks (i.e. communities), this will then pave the way for new types of analysis which are crucial in understanding of the structural and functional properties of the Internet at least at the AS level of abstraction. We thus propose a novel type of analysis of the Internet AS-level topology graph by exploiting the k-clique community denition. First, we show that detected communities can be described by a tree representation. Then we show the presence of two classes of k-clique communities: those that are strictly aected by the nesting process which is embedded in the k-clique community denition, and, on the other hand, those that appear as branches in the tree. We conclude our analysis by highlighting the properties that characterize k-clique communities with dierent k values by exploiting both geographical data and information related to IXPs

k-dense Communities in the Internet AS-Level Topology

Extracting a set of well connected subgraphs as com- munities from the Internet AS-level topology graph is crucially important for assessing the performance of protocols and routing algorithms, for designing ecient networks, and for evaluating the impact of failures. A huge number of community extraction methods have been proposed in the literature, among which the k-core decomposition and the k-clique community extraction methods. The former method is computationally e- cient, but it only discovers coarse-grained and loosely connected communities. On the other hand, k-clique can extract ne-grained and tightly connected communities, but is NP hard and therefore useless for analyzing the Internet AS-level topology graph. In the paper we inves- tigate the Internet structure by exploiting an ecient algorithm for extracting k-dense communities, where a k-clique community implies a k-dense community, which in turn implies a k-core community. The paper provides two innovative contributions. The rst is the application of the k-dense method to the Internet AS-level topology graph - obtained from the CAIDA, DIMES and IRL datasets - to identify well- connected communities and to analyze how these are connected to the rest of the graph. The second contribution relates to the study of the most well-connected communities with the support of two additional datasets: a geographical dataset (which lists, for each AS, the countries in which it has at least one geographical location) and the IXP dataset (which maintains, for each IXP, its geographical position and the list of its participants). We found that the k-max- dense community holds a central position in the Internet AS-level topology graph structure since its 101 ASs (less than the 0.3% of Internet ASs) are involved in more than 39% of all Internet connections. We also found that those ASs are connected to at least one IXP and have at least one geographical location in Europe (only 70.3% of them have at least one additional geographical location outside Europe)

k-Dense communities in the Internet AS-level topology graph

In this paper we investigate the structure of the Internet by exploiting an efficient algorithm for extracting k-dense communities from the Internet AS-level topology graph. The analyses showed that the most well-connected communities consist of a small number of ASs characterized by a high level of clusterization, although they tend to direct a lot of their connections to ASs outside the community. In addition these communities are mainly composed of ASs that participate at the Internet Exchange Points (IXPs) and have a worldwide geographical scope. Regarding k-max-dense ASs we found that they play a primary role in the Internet connectivity since they are involved in a huge number of Internet connections (42% of Internet connections). We also investigated the properties of three classes of k-max-dense ASs: Content Delivery Networks, Internet Backbone Providers and Tier-1s. Specifically, we showed that CDNs and IBPs heavily exploit IXPs by participating in many of them and connecting to many IXP participant ASs. On the other hand, we found that a high percentage of connections originated by Tier-1 ASs are likely to involve national ASs which do not participate at IXPs

A Configurable Protocol for Quantum Entanglement Distribution to End Nodes

The primary task of a quantum repeater network is to deliver entanglement among end nodes. Most of existing entanglement distribution protocols do not consider purification, which is thus delegated to an upper layer. This is a major drawback since, once an end-to-end entangled connection (or a portion thereof) is established it cannot be purified if its fidelity (F) does not fall within an interval bounded by Fmin (greater than 0.5) and Fmax (less than 1). In this paper, we propose the Ranked Entanglement Distribution Protocol (REDiP), a connection-oriented protocol that overcomes the above drawback. This result was achieved by including in our protocol two mechanisms for carrying out jointly purification and entanglement swapping. We use simulations to investigate the impact of these mechanisms on the performance of a repeater network, in terms of throughput and fidelity. Moreover, we show how REDiP can easily be configured to implement custom entanglement swapping and purification strategies, including (but not restricted to) those adopted in two recent works.Comment: 6 pages, 6 figures, submitted to IEEE ICC 202

The Impact of IXPs on the AS-level Topology Structure of the Internet

The AS-level topology of the Internet has been quite a hot research topic in the last few years. However, only a small number of studies have been developed that give a structural interpretation of this graph. Such an interpretation is crucially important in order to test protocols and optimal routing algorithms, to design efficient networks, and for failure detection purposes. Moreover, most research does not highlight the role that IXPs have on the AS-level structure of the Internet, although their role is recognized as fundamental. The initial contribution of this study is an analysis of the most important AS-level topologies that are publicly found on the web and an analysis of the topology obtained when they are merged. We compiled structural information from this topology making considerable use of the k-core decomposition technique to delineate various particular classes of nodes. Next, we associated node properties with a reasonable modus operandi of the ASs on the Internet. The second contribution is a study of the impact that ASs connected to IXPs and BGP connections crossing IXPs have on the AS-level topology. To achieve this, we developed a procedure to gather reliable information related to IXPs and their participants

BGP and inter-AS economic relationships

The structure of the Internet is still unknown even if it pro- vides well-known services for a large part of the worldwide population. Its current conguration is the result of complex economic interaction developed in the last 20 years among important carriers and ISPs (i.e. ASes). Although with slight success, in the last few years some research work tried to shed light on the economic relationships established among ASes. Typical approaches employed in the above work proceed along two lines: rst, data from BGP monitors spread out all over the world is gath- ered to infer an Internet AS-level topology graph, and second heuristics taking as input this graph are applied to get economic tags associated to all edges between nodes (i.e. ASes). In this paper we propose an in- novative tagging approach leveraging on the lifetime of an AS path to infer the economic relationships on all edges joining the ASes crossed by the path itself, without cutting-o backup links, that bring economic information as well as stable links. The major ndings of our approach can be summarized as follows: (data hygiene before infer the Internet AS-level topology graph) study on AS paths loops, human error and their impact on data correctness ( life-time based tagging we do not cut-o bakcup links) we evidence those tags are inferred only from a partial viewpoint we evidence the maximum lifetime of the AS path that have contributed to infer the tag of each connection { classication of candidate Tier-1 AS based on three indexes re ecting the importance of an AS { explanation and life-time study of non valley-free AS path

Optimal joint routing and link scheduling for real-time traffic in TDMA Wireless Mesh Networks

We investigate the problem of joint routing and link scheduling in Time-Division Multiple Access (TDMA) Wireless Mesh Networks (WMNs) carrying real-time traffic. We propose a framework that always computes a feasible solution (i.e. a set of paths and link activations) if there exists one, by optimally solving a mixed integer-non linear problem. Such solution can be computed in minutes or tens thereof for e.g. grids of up to 4x4 nodes. We also propose heuristics based on Lagrangian decomposition to compute suboptimal solutions considerably faster and/or for larger WMNs, up to about 50 nodes. We show that the heuristic solutions are near-optimal, and we exploit them to gain insight on the schedulability in WMN, i.e. to investigate the optimal placement of one or more gateways from a delay bound perspec-tive, and to investigate how the schedulability is affected by the transmission range