The Fundamental Limits of Broadcasting in Dense Wireless Mobile Networks

In this paper, we investigate the fundamental properties of broadcasting in {em mobile} wireless networks. In particular, we characterize broadcast capacity and latency of a mobile network, subject to the condition that the stationary node spatial distribution generated by the mobility model is uniform. We first study the intrinsic properties of broadcasting, and present the {sc RippleCast} broadcasting scheme that simultaneously achieves asymptotically optimal broadcast capacity and latency, subject to a weak upper bound on maximum node velocity and under the assumption of static broadcast source. We then extend {sc RippleCast} with the novel notion of center-casting, and prove that asymptotically optimal broadcast capacity and latency can be achieved also when the broadcast source is mobile. This study intendedly ignores the burden related to the selection of broadcast relay nodes within the mobile network, and shows that optimal broadcasting in mobile networks is, in principle, possible. We then investigate the broadcasting problem when the relay selection burden is taken into account, and present a combined distributed leader election and broadcasting scheme achieving a broadcast capacity and latency which is within a $Theta((log n)^{1+frac{2}{alpha}})$ factor from optimal, where $n$ is the number of mobile nodes and $alpha>2$ is the path loss exponent. However, this result holds only under the assumption that the upper bound on node velocity converges to zero (although with a very slow, poly-logarithmic rate) as $n$ grows to infinity

Combinatorics and Metric Geometry

This thesis consists of an introduction and seven chapters, each devoted to a different combinatorial problem. In Chapters 1 and 2, we consider the main subject of this thesis; the sharp stability of the Brunn-Minkowski inequality (BM). This celebrated theorem from the 19th century asserts that for bodies A,B $\subset$ $\mathbb{R}$$^{k}$, we have |A + B|$^{1/k}$ $\geq$ |A|$^{1/k}$ + |B|$^{1/k}$, where |$\cdot$| is the Lebesgue measure and A + B := {a + b : a $\in$ A, b $\in$ B} is the Minkowski sum. Moreover, we have equality if and only if A,B are homothetic convex sets. The stability question, studied in many papers, asks how the distance to equality in BM relates to the distance from A,B to homothetic convex sets. In particular, given Brunn-Minkowsi deficit $\delta$ := |A+B|$^{1/k}$ / |A|$^{1/k}$ + |B|$^{1/k}$ -1, and normalized volume ratio $\textit{t}$ := |A|$^{1/k}$ / |A|$^{1/k}$ + |B|$^{1/k}$, what is the best bound one can find on $\omega$ := |K$_{A}$ \ A| / |A| + |K$_{B}$ \ B| / |B|, where K$_{A}$ $\supset$ A, and K$_{B}$ $\supset$ B are homothetic convex sets of minimal size? In Chapter 2, we prove a conjecture by Figalli and Jerison establishing the sharp stability for homothetic sets. In particular, we show that for homothetic sets, we have $\omega$ = O$_{k}$($\delta$t$^{-1}$), for $\delta$ sufficiently small. In Chapter 3, we establish the sharp stability for planar sets, i.e. we show that for planar sets and $\delta$ sufficiently small, we have $\omega$ = O($\delta$$^{1/2}$t$^{-1/2}$). A crucial result in Chapter 3 shows that for any $\epsilon$ > 0, if $\delta$ is sufficiently small, then we have |co(A + B) \ (A + B)| $\leq$ (1 + $\epsilon$)(|co(A) \ A| + |co(B) \ B|). In Chapter 4, we consider a reconstruction problem for functions on graphs. Given a function $\textit{f}$:V(G) $\rightarrow$ [k] on the vertices of a graph G and a random walk (U$_{i}$)$^{{\infty}}_{i = 1}$ on that graph, can we reconstruct $\textit{f}$ (up to automorphisms) based on just ($\textit{f}$(U$_{i}$)$^{{\infty}}_{i = 1}$? Gross and Grupel showed this was not generally possible on the hypercube, by constructing non-isomorphic $\textit{locally p-biased}$ sets $\textit{X}$, so that for each vertex $\textit{v}$ the fraction of neighbours which is in $\textit{X}$ is exactly $\textit{p}$. Answering a question of Gross and Grupel, we construct uncountably many non-isomorphic partitions of $\mathbb{Z}$$^{k}$ into 2k parts such that every element of $\mathbb{Z}$$^{k}$ has exactly one neighbour in each part. As a result, we find $\textit{locally p-biased}$ sets for all $\textit{p = c/2n}$ with $\textit{c}$ $\in$ {0, ... , 2n}. In Chapter 5, we prove the complete graph case of the bunkbed conjecture. Given a graph G, let the bunkbed graph BB(G) be the graph G$\Box$K$_{2}$, i.e. the graph obtained from considering two copies of G and connecting equivalent vertices with an edge. The bunkbed conjecture posed by Kasteleyn in 1985 asserts the very intuitive statement that when considering percolation with uniform parameter p, we have $\mathbb{P}$(u$_{1}$ $\leftrightarrow$ v$_{1}$) $\geq$ $\mathbb{P}$(u$_{1}$ $\leftrightarrow$ v$_{2}$), i.e. a vertex has a higher probability of being connected to a vertex in the same copy of G than being connected to the equivalent vertex in the other copy of G. In Chapter 6, we consider the (t,r) broadcast domination number, a generalisation of the domination number in graphs. In this form of domination, we consider a set T $\subset$ V(G) of towers which broadcast at strength t, where broadcast strength decays linearly with distance in the graph. A set of towers is (t,r) broadcast dominating if every vertex in the graph receives at least r signal from all towers combined. More formally, the (t,r) broadcast domination number of a graph G is the minimal cardinality of a set T $\subset$ V(G) such that for every vertex v $\in$ V(G), we have $^{{\Sigma}}_{u {{\in}} T}$ max{t - d(u,v),0} $\geq$ r. Proving a conjecture by Drews, Harris, and Randolph, we establish that the minimal asymptotical density of (t,3) broadcasting subset of $\mathbb{Z}$$^{2}$ is the same as the minimal asymptotical density of a (t-1,1) broadcasting subset of $\mathbb{Z}$$^{2}$. In Chapter 7, we consider the eternal game chromatic number, a version of the game chromatic number in which the game continues after all vertices have been coloured. We show that with high probability $\chi$$^\infty_g$ (G$_{n,p}$) = (p/2 + o(1))n for odd n, and also for even n when p = 1/k for some k $\in$ $\mathbb{N}$. The upper bound applies for even n and any other value of p as well, but we conjecture in this case this upper bound is not sharp. Finally, we answer a question posed by Klostermeyer and Mendoza. In Chapter 8, we consider the bridge-burning cops and robbers game, a version of the game where after a robber moves over an edge, the edge is removed from the graph. Proving a generalization of a conjecture by Kinnersley and Peterson, we establish the asymptotically maximal capture time in this game for graphs with bridge-burning cops number at least three. In particular, we show that this maximal capture time grows as k$^{-O(k)}$n$^{k+2}$, where k $\geq$ 3 is the bridge burning cop number and n is the number of vertices of the graph

A cluster based communication architecture for distributed applications in mobile ad hoc networks

Thesis (Master)--Izmir Institute of Technology, Computer Engineering, Izmir, 2006Includes bibliographical references (leaves: 63-69)Text in English; Abstract: Turkish and Englishx, 85 leavesIn this thesis, we aim to design and implement three protocols on a hierarchical architecture to solve the balanced clustering, backbone formation and distributed mutual exclusion problems for mobile ad hoc network(MANET)s. Our ¯rst goal is to cluster the MANET into balanced partitions. Clustering is a widely used approach to ease implemen-tation of various problems such as routing and resource management in MANETs. We propose the Merging Clustering Algorithm(MCA) for clustering in MANETs that merges clusters to form higher level of clusters by increasing their levels. Secondly, we aim to con-struct a directed ring topology across clusterheads which were selected by MCA. Lastly, we implement the distributed mutual exclusion algorithm based on Ricart-Agrawala algo-rithm for MANETs(Mobile RA). Each cluster is represented by a coordinator node on the ring which implements distributed mutual exclusion algorithm on behalf of any member in the cluster it represents. We show the operations of the algorithms, analyze their time and message complexities and provide results in the simulation environment of ns2

Efficient Data Dissemination in Wireless Ad Hoc Networks

In this thesis, we study the problem of efficient data dissemination in wireless sensor and mobile ad hoc networks. In wireless sensor networks we study two problems: (1) construction of virtual backbones and clustering hierarchies to achieve efficient routing, and (2) placement of multiple sinks, where each sensor is at a bounded distance to several sinks, to analyze and process data before sending it to a central unit. Often connected dominating sets have been used for such purposes. However, a connected dominating set is often vulnerable due to frequent node failures in wireless sensor networks. Hence, to provide a degree of fault-tolerance we consider in problem (1) a 2-connected (k,r)-dominating set, denoted D(2,k,r), to act as a virtual backbone or a clustering hierarchy, and in problem (2) a total (k,r)-dominating set to act as sinks in wireless sensor networks. Ideally, the backbone or the number of sinks in the network should constitute the smallest percentage of nodes in the network. We model the wireless sensor network as a graph. The total (k,r)-dominating set and the 2-connected (k,r)-dominating set have not been studied in the literature. Thus, we propose two centralized approximation algorithms to construct a D(2,k,r) in unit disk graphs and in general graphs. We also derive upper bounds on the total (k,r)-domination number in graphs of girth at least 2k+1 as well as in random graphs with non-fixed probability p. In mobile ad hoc networks we propose a hexagonal based beacon-less flooding algorithm, HBLF, to efficiently flood the network. We give sufficient condition that even in the presence of holes in the network, HBLF achieves full delivery. Lower and upper bounds are given on the number of forwarding nodes returned by HBLF in a network with or without holes. When there are no holes in the network, we show that the ratio of the shortest path returned by HBLF to the shortest path in the network is constant. We also present upper bounds on the broadcast time of HBLF in a network with or without holes

The Design of Medium Access Control (MAC) Protocols for Energy Efficient and QoS Provision in Wireless Sensor Networks

This thesis work focuses on innovative design of media access control (MAC) protocols in wireless sensor networks (WNSs). The characteristics of the WSN inquire that the network service design considers both energy efficiency and the associated application requirement. However, most existing protocols address only the issue of energy efficiency. In this thesis, a MAC protocol has been proposed (referred to as Q-MAC) that not only minimized the energy consumption in multi-hop WSNs, but also provides Quality of Service (QoS) by differentiating network services based on priority levels prescribed by different applications. The priority levels reflect the state of system resources including residual energy and queue occupancies. Q-MAC contains both intra- and inter- node arbitration mechanisms. The intra-node packet scheduling employs a multiple queuing architectures, and applies a scheduling scheme consisting of packet classification and weighted arbitration. We introduce the Power Conservation MACAW (PC-MACAW), a power-aware scheduling mechanism which, together with the Loosely Prioritized Random Access (LPRA) algorithm, govern the inter-node scheduling. Performance evaluation are conducted between Q-MAC and S-MAC with respect to two performance metrics: energy consumption and average latency. Simulation results indicate Q-MAC achieves comparable performance to that of S-MAC in non-prioritized traffic scenarios. When packets with different priorities are introduced, Q-MAC yields noticeable average latency differentiations between the classes of service, while preserving the same degree of energy consumption as that of S-MAC. Since the high density nature of WSN may introduce heavy traffic load and thus consume large amount of energy for communication, another MAC protocol, referred to as the Deployment-oriented MAC (D-MAC)has been further proposed. D-MAC minimalizes both sensing and communication redundancy by putting majority of redundant nodes into the sleep state. The idea is to establish a sensing and communication backbone covering the whole sensing field with the least sensing and communication redundancy. In specific, we use equal-size rectangular cells to partition the sensing field and chose the size of each cell in a way such that regardless of the actual location within the cell, a node can always sense the whole cell and communicate with all the nodes in neighboring cells. Once the sensing field has been partitioned using these cells, a localized Location-aware Selection Algorithm (LSA) is carried out to pick up only one node within each cell to be active for a fixed amount of period. This selection is energy-oriented, only nodes with a maximum energy will be on and the rest of nodes will be put into the sleep state once the selection process is over. To balance the energy consumption, the selection algorithm is periodically conducted until all the nodes are out of power. Simulation results indicated that D-MAC saves around 80% energy compared to that of S-MAC and Q-MAC, while maintaining 99% coverage. D-MAC is also superior to S-MAC and Q-MAC in terms of average latency. However, the use of GPS in D-MAC in identifying the nodes within the same cell, would cause extra cost and complexity for the design of sensor nodes

Improving the design of wireless sensor networks using QoS-aware opportunistic techniques

The design of a Wireless Sensor Network with QoS is a challenging and complex topic especially when the post-deployment corrections are expensive. This paper proposes a design methodology of Wireless Sensor Networks to estimate network performance in terms of end-to-end delay and reliability. It uses a probabilistic model to determine the needed node density, then adopting a variant of geographic routing it lets to calculate the number of path hops. The introduced opportunistic mechanism offers a trade-off between low end-to-end delay and reliable packets delivery. The modeled network with the adopted Geographic Opportunistic Routing has been evaluated through simulations and some guidelines about its design in order to obtain desired performance are given

A survey on energy efficient techniques in wireless sensor networks

International audienceThe myriad of potential applications supported by wireless sensor networks (WSNs) has generated much interest from the research community. Various applications range from small size low industrial monitoring to large scale energy constrained environmental monitoring. In all cases, an operational network is required to fulfill the application missions. In addition, energy consumption of nodes is a great challenge in order to maximize network lifetime. Unlike other networks, it can be hazardous, very expensive or even impossible to charge or replace exhausted batteries due to the hostile nature of environment. Researchers are invited to design energy efficient protocols while achieving the desired network operations. This paper focuses on different techniques to reduce the consumption of the limited energy budget of sensor nodes. After having identified the reasons of energy waste in WSNs, we classify energy efficient techniques into five classes, namely data reduction, control reduction, energy efficient routing, duty cycling and topology control. We then detail each of them, presenting subdivisions and giving many examples. We conclude by a recapitulative table

Mobile Ad Hoc Networks

Guiding readers through the basics of these rapidly emerging networks to more advanced concepts and future expectations, Mobile Ad hoc Networks: Current Status and Future Trends identifies and examines the most pressing research issues in Mobile Ad hoc Networks (MANETs). Containing the contributions of leading researchers, industry professionals, and academics, this forward-looking reference provides an authoritative perspective of the state of the art in MANETs. The book includes surveys of recent publications that investigate key areas of interest such as limited resources and the mobility of mobile nodes. It considers routing, multicast, energy, security, channel assignment, and ensuring quality of service. Also suitable as a text for graduate students, the book is organized into three sections: Fundamentals of MANET Modeling and Simulation—Describes how MANETs operate and perform through simulations and models Communication Protocols of MANETs—Presents cutting-edge research on key issues, including MAC layer issues and routing in high mobility Future Networks Inspired By MANETs—Tackles open research issues and emerging trends Illustrating the role MANETs are likely to play in future networks, this book supplies the foundation and insight you will need to make your own contributions to the field. It includes coverage of routing protocols, modeling and simulations tools, intelligent optimization techniques to multicriteria routing, security issues in FHAMIPv6, connecting moving smart objects to the Internet, underwater sensor networks, wireless mesh network architecture and protocols, adaptive routing provision using Bayesian inference, and adaptive flow control in transport layer using genetic algorithms