MAP: Medial Axis Based Geometric Routing in Sensor Networks

One of the challenging tasks in the deployment of dense wireless networks (like sensor networks) is in devising a routing scheme for node to node communication. Important consideration includes scalability, routing complexity, the length of the communication paths and the load sharing of the routes. In this paper, we show that a compact and expressive abstraction of network connectivity by the medial axis enables efficient and localized routing. We propose MAP, a Medial Axis based naming and routing Protocol that does not require locations, makes routing decisions locally, and achieves good load balancing. In its preprocessing phase, MAP constructs the medial axis of the sensor field, defined as the set of nodes with at least two closest boundary nodes. The medial axis of the network captures both the complex geometry and non-trivial topology of the sensor field. It can be represented compactly by a graph whose size is comparable with the complexity of the geometric features (e.g., the number of holes). Each node is then given a name related to its position with respect to the medial axis. The routing scheme is derived through local decisions based on the names of the source and destination nodes and guarantees delivery with reasonable and natural routes. We show by both theoretical analysis and simulations that our medial axis based geometric routing scheme is scalable, produces short routes, achieves excellent load balancing, and is very robust to variations in the network model

Optimal Spanners for Unit Ball Graphs in Doubling Metrics

Resolving an open question from 2006, we prove the existence of light-weight bounded-degree spanners for unit ball graphs in the metrics of bounded doubling dimension, and we design a simple $\mathcal{O}(\log^*n)$-round distributed algorithm in the LOCAL model of computation, that given a unit ball graph $G$ with $n$ vertices and a positive constant $\epsilon < 1$ finds a $(1+\epsilon)$-spanner with constant bounds on its maximum degree and its lightness using only 2-hop neighborhood information. This immediately improves the best prior lightness bound, the algorithm of Damian, Pandit, and Pemmaraju, which runs in $\mathcal{O}(\log^*n)$ rounds in the LOCAL model, but has a $\mathcal{O}(\log \Delta)$ bound on its lightness, where $\Delta$ is the ratio of the length of the longest edge to the length of the shortest edge in the unit ball graph. Next, we adjust our algorithm to work in the CONGEST model, without changing its round complexity, hence proposing the first spanner construction for unit ball graphs in the CONGEST model of computation. We further study the problem in the two dimensional Euclidean plane and we provide a construction with similar properties that has a constant average number of edge intersections per node. Lastly, we provide experimental results that confirm our theoretical bounds, and show an efficient performance from our distributed algorithm compared to the best known centralized construction

Distributed Construction of Lightweight Spanners for Unit Ball Graphs

Resolving an open question from 2006 [Damian et al., 2006], we prove the existence of light-weight bounded-degree spanners for unit ball graphs in the metrics of bounded doubling dimension, and we design a simple ?(log^*n)-round distributed algorithm in the LOCAL model of computation, that given a unit ball graph G with n vertices and a positive constant ? < 1 finds a (1+?)-spanner with constant bounds on its maximum degree and its lightness using only 2-hop neighborhood information. This immediately improves the best prior lightness bound, the algorithm of Damian, Pandit, and Pemmaraju [Damian et al., 2006], which runs in ?(log^*n) rounds in the LOCAL model, but has a ?(log ?) bound on its lightness, where ? is the ratio of the length of the longest edge to the length of the shortest edge in the unit ball graph. Next, we adjust our algorithm to work in the CONGEST model, without changing its round complexity, hence proposing the first spanner construction for unit ball graphs in the CONGEST model of computation. We further study the problem in the two dimensional Euclidean plane and we provide a construction with similar properties that has a constant average number of edge intersections per node. Lastly, we provide experimental results that confirm our theoretical bounds, and show an efficient performance from our distributed algorithm compared to the best known centralized construction

07151 Abstracts Collection -- Geometry in Sensor Networks

From 9.4.2007 to 13.4.07, the Dagstuhl Seminar 07151 ``Geometry in Sensor Networks\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Intrusion detection in IPv6-enabled sensor networks.

In this research, we study efficient and lightweight Intrusion Detection Systems (IDS) for ad-hoc networks through the lens of IPv6-enabled Wireless Sensor Actuator Networks. These networks consist of highly constrained devices able to communicate wirelessly in an ad-hoc fashion, thus following the architecture of ad-hoc networks. Current state of the art IDS in IoT and WSNs have been developed considering the architecture of conventional computer networks, and as such they do not efficiently address the paradigm of ad-hoc networks, which is highly relevant in emerging network paradigms, such as the Internet of Things (IoT). In this context, the network properties of resilience and redundancy have not been extensively studied. In this thesis, we first identify a trade-off between the communication and energy overheads of an IDS (as captured by the number of active IDS agents in the network) and the performance of the system in terms of successfully identifying attacks. In order to fine-tune this trade-off, we model networks as Random Geometric Graphs; these are a rigorous approach that allows us to capture underlying structural properties of the network. We then introduce a novel IDS architectural approach that consists of a central IDS agent and set of distributed IDS agents deployed uniformly at random over the network area. These nodes are able to efficiently detect attacks at the networking layer in a collaborative manner by monitoring locally available network information provided by IoT routing protocols, such as RPL. The detailed experimental evaluation conducted in this research demonstrates significant performance gains in terms of communication overhead and energy dissipation while maintaining high detection rates. We also show that the performance of our IDS in ad-hoc networks does not rely on the size of the network but on fundamental underling network properties, such as the network topology and the average degree of the nodes. The experiments show that our proposed IDS architecture is resilient against frequent topology changes due to node failures

Scalable Routing Easy as PIE: a Practical Isometric Embedding Protocol (Technical Report)

We present PIE, a scalable routing scheme that achieves 100% packet delivery and low path stretch. It is easy to implement in a distributed fashion and works well when costs are associated to links. Scalability is achieved by using virtual coordinates in a space of concise dimensionality, which enables greedy routing based only on local knowledge. PIE is a general routing scheme, meaning that it works on any graph. We focus however on the Internet, where routing scalability is an urgent concern. We show analytically and by using simulation that the scheme scales extremely well on Internet-like graphs. In addition, its geometric nature allows it to react efficiently to topological changes or failures by finding new paths in the network at no cost, yielding better delivery ratios than standard algorithms. The proposed routing scheme needs an amount of memory polylogarithmic in the size of the network and requires only local communication between the nodes. Although each node constructs its coordinates and routes packets locally, the path stretch remains extremely low, even lower than for centralized or less scalable state-of-the-art algorithms: PIE always finds short paths and often enough finds the shortest paths.Comment: This work has been previously published in IEEE ICNP'11. The present document contains an additional optional mechanism, presented in Section III-D, to further improve performance by using route asymmetry. It also contains new simulation result

JGraphT -- A Java library for graph data structures and algorithms

Mathematical software and graph-theoretical algorithmic packages to efficiently model, analyze and query graphs are crucial in an era where large-scale spatial, societal and economic network data are abundantly available. One such package is JGraphT, a programming library which contains very efficient and generic graph data-structures along with a large collection of state-of-the-art algorithms. The library is written in Java with stability, interoperability and performance in mind. A distinctive feature of this library is the ability to model vertices and edges as arbitrary objects, thereby permitting natural representations of many common networks including transportation, social and biological networks. Besides classic graph algorithms such as shortest-paths and spanning-tree algorithms, the library contains numerous advanced algorithms: graph and subgraph isomorphism; matching and flow problems; approximation algorithms for NP-hard problems such as independent set and TSP; and several more exotic algorithms such as Berge graph detection. Due to its versatility and generic design, JGraphT is currently used in large-scale commercial, non-commercial and academic research projects. In this work we describe in detail the design and underlying structure of the library, and discuss its most important features and algorithms. A computational study is conducted to evaluate the performance of JGraphT versus a number of similar libraries. Experiments on a large number of graphs over a variety of popular algorithms show that JGraphT is highly competitive with other established libraries such as NetworkX or the BGL.Comment: Major Revisio

An Architecture for Resilient Intrusion Detection in Ad-hoc Networks

We study efficient and lightweight Intrusion Detection Systems (IDS) for ad-hoc networks via the prism of IPv6-enabled Wireless Sensor Actuator Networks. These networks consist of highly constrained devices able to communicate wirelessly in an ad-hoc fashion, thus following the architecture of ad-hoc networks. Current state-of-the-art (IDS) has been developed taking into consideration the architecture of conventional computer networks, and as such they do not efficiently address the paradigm of ad-hoc networks, that is highly relevant in emergent networks, such as the Internet of Things (IoT). In this context, the network properties of resilience and redundancy have not been studied yet. In this work, we firstly identify a trade-off between the communication overhead and energy consumption of an IDS (as captured by the number of active IDS agents in the network) and the performance of the system in terms of successfully identifying attacks. In order to fine tune this trade-off, we model such networks as Random Geometric Graphs; a rigorous approach that allows us to capture underlying structural properties of the network. We then introduce a novel IDS architectural approach that consists of a central IDS agent a set of distributed IDS agents deployed uniformly at random over the network area. These nodes are able to efficiently detect attacks at the networking layer in a collaborative manner by monitoring locally available network information provided by IoT routing protocols such as RPL. Our detailed experimental evaluation demonstrates significant performance gains in terms of communication overhead and energy consumption while maintaining high detection rates. We also show that the performance of our IDS in ad-hoc networks does not rely on the size of the network but on fundamental underling network properties, such as the network topology and the average degree of the nodes. Conducted experiments show that our proposed IDS architecture is resilient against frequent topology changes due to nodes failures

Efficient collection of sensor data via a new accelerated random walk

Motivated by the problem of efficiently collecting data from wireless sensor networks via a mobile sink, we present an accelerated random walk on random geometric graphs (RGG). Random walks in wireless sensor networks can serve as fully local, lightweight strategies for sink motion that significantly reduce energy dissipation but introduce higher latency in the data collection process. In most cases, random walks are studied on graphs like Gn,p and grid. Instead, we here choose the RGG model, which abstracts more accurately spatial proximity in a wireless sensor network. We first evaluate an adaptive walk (the random walk with inertia) on the RGG model; its performance proved to be poor and led us to define and experimentally evaluate a novel random walk that we call γ-stretched random walk. Its basic idea is to favour visiting distant neighbours of the current node towards reducing node overlap and accelerate the cover time. We also define a new performance metric called proximity cover time that, along with other metrics such as visit overlap statistics and proximity variation, we use to evaluate the performance properties and features of the various walks