Topological measures for the analysis of wireless sensor networks

Concepts such as energy dependence, random deployment, dynamic topological update, self-organization, varying large number of nodes are among many factors that make WSNs a type of complex system. However, when analyzing WSNs properties using complex network tools, classical topological measures must be considered with care as they might not be applicable in their original form. In this work, we focus on the topological measures frequently used in the related field of Internet topological analysis. We illustrate their applicability to the WSNs domain through simulation experiments. In the cases when the classic metrics turn out to be incompatible, we propose some alternative measures and discuss them based on the WSNs characteristics.Comment: 3rd International Conference on Ambient Systems (ANT), Networks and Technologies, Niagara Falls : Canada (2012

Compact Routing on Internet-Like Graphs

The Thorup-Zwick (TZ) routing scheme is the first generic stretch-3 routing scheme delivering a nearly optimal local memory upper bound. Using both direct analysis and simulation, we calculate the stretch distribution of this routing scheme on random graphs with power-law node degree distributions, $P_k \sim k^{-\gamma}$. We find that the average stretch is very low and virtually independent of $\gamma$. In particular, for the Internet interdomain graph, $\gamma \sim 2.1$, the average stretch is around 1.1, with up to 70% of paths being shortest. As the network grows, the average stretch slowly decreases. The routing table is very small, too. It is well below its upper bounds, and its size is around 50 records for $10^4$-node networks. Furthermore, we find that both the average shortest path length (i.e. distance) $\bar{d}$ and width of the distance distribution $\sigma$ observed in the real Internet inter-AS graph have values that are very close to the minimums of the average stretch in the $\bar{d}$- and $\sigma$-directions. This leads us to the discovery of a unique critical quasi-stationary point of the average TZ stretch as a function of $\bar{d}$ and $\sigma$. The Internet distance distribution is located in a close neighborhood of this point. This observation suggests the analytical structure of the average stretch function may be an indirect indicator of some hidden optimization criteria influencing the Internet's interdomain topology evolution.Comment: 29 pages, 16 figure

Economizing ISP Interconnections at Internet Exchange Points

The Internet service provider market is very competitive. Small and medium-size Internet service providers (ISPs) are competing for customers, while, at the same time, they are under price pressure from upstream providers. Therefore, these ISPs have to reduce their overall cost of interconnection. In order to address this issue, Internet exchange points (IXPs) have been built up in recent years, which allow small and medium-size ISPs to go into public or private peering with other ISPs. However, those ISPs do not have sufficient information to select the optimal set of ISPs, with which they should go into private peering agreements. In this paper, we describe an approach, which provides ISPs with the information about the most economical interconnections to other ISPs. This approach helps small and medium-size Internet service providers to reduce their interconnection costs for upstream connectivity and to improve network performance for their customers. To achieve that, our approach uses Internet topology information in close neighborhood of the ISP (which is determined by the set of ISPs connected to the IXP), measurement information about the number of bytes transmitted, and traffic pricing schemes. Based on real data, our analysis results demonstrate that our approach provides the necessary information to ISPs for locally optimizing their interconnection agreements (e.g. peering, sibling, transit agreements)

Analysis of beacon triangulation in random graphs

Our research focusses on the problem of finding nearby peers in the Internet. We focus on one particular approach, Beacon Triangulation that is widely used to solve the peer-finding problem. Beacon Triangulation is based on relative distances of nodes to some special nodes called beacons. The scheme gives an error when a new node that wishes to join the network has the same relative distance to two or more nodes. One of the reasons for the error is that two or more nodes have the same distance vectors. As a part of our research work, we derive the conditions to ensure the uniqueness of distance vectors in any network given the shortest path distribution of nodes in that network. We verify our analytical results for G(n, p) graphs and the Internet. We also derive other conditions under which the error in the Beacon Triangulation scheme reduces to zero. We compare the Beacon Triangulation scheme to another well-known distance estimation scheme known as Global Network Positioning (GNP)

An analysis of spatial percolation structures using a network approach

Includes bibliographical references.In this thesis we analyse several spatial structures, built from percolation models, by means of an approach used so far in the field of network science. In the first chapter we summarize the major network concepts and characterizations that have been obtained as regards the statistical properties of several data sets or theoretical models, We also give a brief introduction to percolation theory and its applications, adding details in two particular cases where mathematical results are available. In the second chapter we then study one particular application of percolation theory to the modelling of distribution and species abundance at different seales. We mainly focus on the way percolation theory was used to compare two diffcrcnt spatial patterns, particularly the random and the aggrergated distribution