Asynchronous Local Construction of Bounded-Degree Network Topologies Using Only Neighborhood Information

We consider ad-hoc networks consisting of $n$ wireless nodes that are located on the plane. Any two given nodes are called neighbors if they are located within a certain distance (communication range) from one another. A given node can be directly connected to any one of its neighbors and picks its connections according to a unique topology control algorithm that is available at every node. Given that each node knows only the indices (unique identification numbers) of its one- and two-hop neighbors, we identify an algorithm that preserves connectivity and can operate without the need of any synchronization among nodes. Moreover, the algorithm results in a sparse graph with at most $5n$ edges and a maximum node degree of $10$. Existing algorithms with the same promises further require neighbor distance and/or direction information at each node. We also evaluate the performance of our algorithm for random networks. In this case, our algorithm provides an asymptotically connected network with $n(1+o(1))$ edges with a degree less than or equal to $6$ for $1-o(1)$ fraction of the nodes. We also introduce another asynchronous connectivity-preserving algorithm that can provide an upper bound as well as a lower bound on node degrees.Comment: To appear in IEEE Transactions on Communication

Position-based routing algorithms for three-dimensional ad hoc networks

In position-based routing algorithms, the nodes use the geographical information to make routing decisions. Recent research in this field addresses such routing algorithms in two-dimensional (2 D ) space. However, in real applications, the nodes may be distributed in three-dimensional (3 D ) space. Transition from 2 D to 3 D is not always easy, since many problems in 3 D are significantly harder than their 2 D counterparts. This dissertation focuses on providing a reliable and efficient position-based routing algorithms with the associated pre-processing algorithms for various 3 D ad hoc networks. In the first part of this thesis, we propose a generalization of the Yao graph where the cones used are adaptively centered on the nearest set of neighbors for each node, thus creating a directed or undirected spanning subgraph of a given unit disk graph (UDG). We show that these locally constructed spanning subgraphs are strongly connected, have bounded out-degree, are t -spanners with bounded stretch factor, contain the Euclidean minimum spanning tree as a subgraph, and are orientation-invariant. Then we propose the first local, constant time algorithm that constructs an independent dominating set and connected dominating set of a Unit Disk Graph in a 3 D environment. We present a truncated octahedral tiling system of the space to assign to each node a class number depending on the position of the node within the tiling system. Then, based on the tiling system, we present our local algorithms for constructing the dominating sets. The new algorithms have a constant time complexity and have approximation bounds that are completely independent of the size of the network. In the second part of this thesis, we implement 3 D versions of many current 2 D position-based routing algorithms in addition to creating many new algorithms that are specially designed for a 3 D environment. We show experimentally that these new routing algorithms can achieve nearly guaranteed delivery while discovering routes significantly closer in length to a shortest path. Because many existing position-based routing algorithms for ad hoc and sensor networks use the maximum transmission power of the nodes to discover neighbors, which is a very power-consuming process. We propose several localized power-aware 3 D position-based routing algorithms that increase the lifetime of a network by maximizing the average lifetime of its nodes. These new algorithms use the idea of replacing the constant transmission power of a node with an adjusted transmission power during two stages. The simulation results show a significant improvement in the overall network lifetime over the current power-aware routing algorithm

Distributed optimization algorithms for multihop wireless networks

Recent technological advances in low-cost computing and communication hardware design have led to the feasibility of large-scale deployments of wireless ad hoc and sensor networks. Due to their wireless and decentralized nature, multihop wireless networks are attractive for a variety of applications. However, these properties also pose significant challenges to their developers and therefore require new types of algorithms. In cases where traditional wired networks usually rely on some kind of centralized entity, in multihop wireless networks nodes have to cooperate in a distributed and self-organizing manner. Additional side constraints, such as energy consumption, have to be taken into account as well. This thesis addresses practical problems from the domain of multihop wireless networks and investigates the application of mathematically justified distributed algorithms for solving them. Algorithms that are based on a mathematical model of an underlying optimization problem support a clear understanding of the assumptions and restrictions that are necessary in order to apply the algorithm to the problem at hand. Yet, the algorithms proposed in this thesis are simple enough to be formulated as a set of rules for each node to cooperate with other nodes in the network in computing optimal or approximate solutions. Nodes communicate with their neighbors by sending messages via wireless transmissions. Neither the size nor the number of messages grows rapidly with the size of the network. The thesis represents a step towards a unified understanding of the application of distributed optimization algorithms to problems from the domain of multihop wireless networks. The problems considered serve as examples for related problems and demonstrate the design methodology of obtaining distributed algorithms from mathematical optimization methods

Virtual backbone formation in wireless ad hoc networks

We study the problem of virtual backbone formation in wireless ad hoc networks. A virtual backbone provides a hierarchical infrastructure that can be used to address important challenges in ad hoc networking such as efficient routing, multicasting/broadcasting, activity-scheduling, and energy efficiency. Given a wireless ad hoc network with symmetric links represented by a unit disk graph G = (V, E ), one way to construct this backbone is by finding a Connected Dominating Set (CDS) in G , which is a subset V' ✹ V such that for every node u, u is either in V' or has a neighbor in V' and the subgraph induced by V' is connected. In a wireless ad hoc network with asymmetric links represented by a directed graph G = (V, E ), finding such a backbone translates to constructing a Strongly Connected Dominating and Absorbent Set (SCDAS) in G . An SCDAS is a subset of nodes V' ✹ V such that every node u is either in V' or has an outgoing and an incoming neighbor in V' , and the subgraph induced by V' is strongly connected. Based on most of its applications, minimizing the size of the virtual backbone is an important objective. Therefore, we are interested in constructing CDSs and SCDASs of minimal size. We give efficient distributed algorithms with linear time and message complexities for the construction of the CDS in ad hoc networks with symmetric links. Since topology changes are quite frequent in most ad hoc networks, we propose schemes to locally maintain the CDS in the face of such changes. We also give a distributed algorithm for the construction of the SCDAS in ad hoc networks with asymmetric links. Extensive simulations show that our algorithms outperform all previously known algorithms in terms of the size of the constructed sets

Dynamics of spectral algorithms for distributed routing

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 109-117).In the past few decades distributed systems have evolved from man-made machines to organically changing social, economic and protein networks. This transition has been overwhelming in many ways at once. Dynamic, heterogeneous, irregular topologies have taken the place of static, homogeneous, regular ones. Asynchronous, ad hoc peer-to-peer networks have replaced carefully engineered super-computers, governed by globally synchronized clocks. Modern network scales have demanded distributed data structures in place of traditionally centralized ones. While the core problems of routing remain mostly unchanged, the sweeping changes of the computing environment invoke an altogether new science of algorithmic and analytic techniques. It is these techniques that are the focus of the present work. We address the re-design of routing algorithms in three classical domains: multi-commodity routing, broadcast routing and all-pairs route representation. Beyond their practical value, our results make pleasing contributions to Mathematics and Theoretical Computer Science. We exploit surprising connections to NP-hard approximation, and we introduce new techniques in metric embeddings and spectral graph theory. The distributed computability of "oblivious routes", a core combinatorial property of every graph and a key ingredient in route engineering, opens interesting questions in the natural and experimental sciences as well. Oblivious routes are "universal" communication pathways in networks which are essentially unique. They are magically robust as their quality degrades smoothly and gracefully with changes in topology or blemishes in the computational processes. While we have only recently learned how to find them algorithmically, their power begs the question whether naturally occurring networks from Biology to Sociology to Economics have their own mechanisms of finding and utilizing these pathways. Our discoveries constitute a significant progress towards the design of a self-organizing Internet, whose infrastructure is fueled entirely by its participants on an equal citizen basis. This grand engineering challenge is believed to be a potential technological solution to a long line of pressing social and human rights issues in the digital age. Some prominent examples include non-censorship, fair bandwidth allocation, privacy and ownership of social data, the right to copy information, non-discrimination based on identity, and many others.by Petar Maymounkov.Ph.D

Graph-theoretic channel modeling and topology control protocols for wireless sensor networks

This report addresses two different research problems: (i) It presents a wireless channel model that reduces the complexity associated with high order Markov chains; and (ii) presents energy efficient topology control protocols which provide reliability while maintaining the topology in an energy efficient manner. For the above problems, real wireless sensor network traces were collected and extensive simulations were performed for evaluating the proposed protocols. Accurate simulation and analysis of wireless networks are inherently dependent on accurate models which are able to provide real-time channel characterization. High-order Markov chains are typically used to model errors and losses over wireless channels. However, complexity (i.e., the number of states) of a high-order Markov model increases exponentially with the memory-length of the underlying channel. In this report, a novel graph-theoretic methodology that uses Hamiltonian circuits to reduce the complexity of a high-order Markov model to a desired state budget is presented. The implication of unused states in complexity reduction of higher order Markov model is also explained. The trace-driven performance evaluations for real wireless local area network (WLAN) and wireless sensor network (WSN) channels demonstrate that the proposed Hamiltonian Model, while providing orders of magnitude reduction in complexity, renders an accuracy that is comparable to the Markov model and better than the existing reduced state models. Furthermore, a methodology to preserve energy is presented to increase the network lifetime by reducing the node degree forming an active backbone while considering network connectivity. However, in energy stringent wireless sensor networks, it is of utmost importance to construct the reduced topology with the minimal control overhead. Moreover, most wireless links in practice are lossy links with connectivity probability which desires that a routing protocol provides routing flexibility and reliability at a minimum energy consumption cost. For this purpose, distributed and semi-distributed novel graph-theoretic topology construction protocols are presented that exploit cliques and polygons in a WSN to achieve energy efficiency and reliability. The proposed protocols also facilitate load rotation under topology maintenance, thereby extending the network lifetime. In addition to the above, the report also evaluates why the backbone construction using connected dominating set (CDS) in certain cases remains unable to provide connected sensing coverage in the area covered. For this purpose, a novel protocol that reduces the topology while considering sensing area coverage is presented

Algorithms and complexity analyses for some combinational optimization problems

The main focus of this dissertation is on classical combinatorial optimization problems in two important areas: scheduling and network design. In the area of scheduling, the main interest is in problems in the master-slave model. In this model, each machine is either a master machine or a slave machine. Each job is associated with a preprocessing task, a slave task and a postprocessing task that must be executed in this order. Each slave task has a dedicated slave machine. All the preprocessing and postprocessing tasks share a single master machine or the same set of master machines. A job may also have an arbitrary release time before which the preprocessing task is not available to be processed. The main objective in this dissertation is to minimize the total completion time or the makespan. Both the complexity and algorithmic issues of these problems are considered. It is shown that the problem of minimizing the total completion time is strongly NP-hard even under severe constraints. Various efficient algorithms are designed to minimize the total completion time under various scenarios. In the area of network design, the survivable network design problems are studied first. The input for this problem is an undirected graph G = (V, E), a non-negative cost for each edge, and a nonnegative connectivity requirement ruv for every (unordered) pair of vertices &ruv. The goal is to find a minimum-cost subgraph in which each pair of vertices u,v is joined by at least ruv edge (vertex)-disjoint paths. A Polynomial Time Approximation Scheme (PTAS) is designed for the problem when the graph is Euclidean and the connectivity requirement of any point is at most 2. PTASs or Quasi-PTASs are also designed for 2-edge-connectivity problem and biconnectivity problem and their variations in unweighted or weighted planar graphs. Next, the problem of constructing geometric fault-tolerant spanners with low cost and bounded maximum degree is considered. The first result shows that there is a greedy algorithm which constructs fault-tolerant spanners having asymptotically optimal bounds for both the maximum degree and the total cost at the same time. Then an efficient algorithm is developed which finds fault-tolerant spanners with asymptotically optimal bound for the maximum degree and almost optimal bound for the total cost