4,992 research outputs found
Hierarchical Organization in Complex Networks
Many real networks in nature and society share two generic properties: they
are scale-free and they display a high degree of clustering. We show that these
two features are the consequence of a hierarchical organization, implying that
small groups of nodes organize in a hierarchical manner into increasingly large
groups, while maintaining a scale-free topology. In hierarchical networks the
degree of clustering characterizing the different groups follows a strict
scaling law, which can be used to identify the presence of a hierarchical
organization in real networks. We find that several real networks, such as the
World Wide Web, actor network, the Internet at the domain level and the
semantic web obey this scaling law, indicating that hierarchy is a fundamental
characteristic of many complex systems
K-core decomposition of Internet graphs: hierarchies, self-similarity and measurement biases
We consider the -core decomposition of network models and Internet graphs
at the autonomous system (AS) level. The -core analysis allows to
characterize networks beyond the degree distribution and uncover structural
properties and hierarchies due to the specific architecture of the system. We
compare the -core structure obtained for AS graphs with those of several
network models and discuss the differences and similarities with the real
Internet architecture. The presence of biases and the incompleteness of the
real maps are discussed and their effect on the -core analysis is assessed
with numerical experiments simulating biased exploration on a wide range of
network models. We find that the -core analysis provides an interesting
characterization of the fluctuations and incompleteness of maps as well as
information helping to discriminate the original underlying structure
Understanding Internet topology: principles, models, and validation
Building on a recent effort that combines a first-principles approach to modeling router-level connectivity with a more pragmatic use of statistics and graph theory, we show in this paper that for the Internet, an improved understanding of its physical infrastructure is possible by viewing the physical connectivity as an annotated graph that delivers raw connectivity and bandwidth to the upper layers in the TCP/IP protocol stack, subject to practical constraints (e.g., router technology) and economic considerations (e.g., link costs). More importantly, by relying on data from Abilene, a Tier-1 ISP, and the Rocketfuel project, we provide empirical evidence in support of the proposed approach and its consistency with networking reality. To illustrate its utility, we: 1) show that our approach provides insight into the origin of high variability in measured or inferred router-level maps; 2) demonstrate that it easily accommodates the incorporation of additional objectives of network design (e.g., robustness to router failure); and 3) discuss how it complements ongoing community efforts to reverse-engineer the Internet
Low Cost Quality of Service Multicast Routing in High Speed Networks
Many of the services envisaged for high speed networks, such as B-ISDN/ATM, will support real-time applications with large numbers of users. Examples of these types of application range from those used by closed groups, such as private video meetings or conferences, where all participants must be known to the sender, to applications used by open groups, such as video lectures, where partcipants need not be known by the sender. These types of application will require high volumes of network resources in addition to the real-time delay constraints on data delivery. For these reasons, several multicast routing heuristics have been proposed to support both interactive and distribution multimedia services, in high speed networks. The objective of such heuristics is to minimise the multicast tree cost while maintaining a real-time bound on delay. Previous evaluation work has compared the relative average performance of some of these heuristics and concludes that they are generally efficient, although some perform better for small multicast groups and others perform better for larger groups. Firstly, we present a detailed analysis and evaluation of some of these heuristics which illustrates that in some situations their average performance is reversed; a heuristic that in general produces efficient solutions for small multicasts may sometimes produce a more efficient solution for a particular large multicast, in a specific network. Also, in a limited number of cases using Dijkstra's algorithm produces the best result. We conclude that the efficiency of a heuristic solution depends on the topology of both the network and the multicast, and that it is difficult to predict. Because of this unpredictability we propose the integration of two heuristics with Dijkstra's shortest path tree algorithm to produce a hybrid that consistently generates efficient multicast solutions for all possible multicast groups in any network. These heuristics are based on Dijkstra's algorithm which maintains acceptable time complexity for the hybrid, and they rarely produce inefficient solutions for the same network/multicast. The resulting performance attained is generally good and in the rare worst cases is that of the shortest path tree. The performance of our hybrid is supported by our evaluation results. Secondly, we examine the stability of multicast trees where multicast group membership is dynamic. We conclude that, in general, the more efficient the solution of a heuristic is, the less stable the multicast tree will be as multicast group membership changes. For this reason, while the hybrid solution we propose might be suitable for use with closed user group multicasts, which are likely to be stable, we need a different approach for open user group multicasting, where group membership may be highly volatile. We propose an extension to an existing heuristic that ensures multicast tree stability where multicast group membership is dynamic. Although this extension decreases the efficiency of the heuristics solutions, its performance is significantly better than that of the worst case, a shortest path tree. Finally, we consider how we might apply the hybrid and the extended heuristic in current and future multicast routing protocols for the Internet and for ATM Networks.
Router-level community structure of the Internet Autonomous Systems
The Internet is composed of routing devices connected between them and
organized into independent administrative entities: the Autonomous Systems. The
existence of different types of Autonomous Systems (like large connectivity
providers, Internet Service Providers or universities) together with
geographical and economical constraints, turns the Internet into a complex
modular and hierarchical network. This organization is reflected in many
properties of the Internet topology, like its high degree of clustering and its
robustness.
In this work, we study the modular structure of the Internet router-level
graph in order to assess to what extent the Autonomous Systems satisfy some of
the known notions of community structure. We show that the modular structure of
the Internet is much richer than what can be captured by the current community
detection methods, which are severely affected by resolution limits and by the
heterogeneity of the Autonomous Systems. Here we overcome this issue by using a
multiresolution detection algorithm combined with a small sample of nodes. We
also discuss recent work on community structure in the light of our results
Efficient Micro-Mobility using Intra-domain Multicast-based Mechanisms (M&M)
One of the most important metrics in the design of IP mobility protocols is
the handover performance. The current Mobile IP (MIP) standard has been shown
to exhibit poor handover performance. Most other work attempts to modify MIP to
slightly improve its efficiency, while others propose complex techniques to
replace MIP. Rather than taking these approaches, we instead propose a new
architecture for providing efficient and smooth handover, while being able to
co-exist and inter-operate with other technologies. Specifically, we propose an
intra-domain multicast-based mobility architecture, where a visiting mobile is
assigned a multicast address to use while moving within a domain. Efficient
handover is achieved using standard multicast join/prune mechanisms. Two
approaches are proposed and contrasted. The first introduces the concept
proxy-based mobility, while the other uses algorithmic mapping to obtain the
multicast address of visiting mobiles. We show that the algorithmic mapping
approach has several advantages over the proxy approach, and provide mechanisms
to support it. Network simulation (using NS-2) is used to evaluate our scheme
and compare it to other routing-based micro-mobility schemes - CIP and HAWAII.
The proactive handover results show that both M&M and CIP shows low handoff
delay and packet reordering depth as compared to HAWAII. The reason for M&M's
comparable performance with CIP is that both use bi-cast in proactive handover.
The M&M, however, handles multiple border routers in a domain, where CIP fails.
We also provide a handover algorithm leveraging the proactive path setup
capability of M&M, which is expected to outperform CIP in case of reactive
handover.Comment: 12 pages, 11 figure
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