We study an efficient broadcast scheme in mobile ad hoc networks (MANETs). The objective is to determine a small set of forward nodes to ensure full coverage. We first study several methods that guarantee coverage when the local view of each node on its neighborhood information is updated in a timely manner. Then we consider a general case where nodes move even during the broadcast process, making it impractical to maintain up-to-date and consistent local views. A formal framework is used to model inaccurate local views in MANETs, where full coverage is guaranteed if three sufficient conditions, connectivity, link availability, and consistency, are met. Three solutions are proposed to satisfy those conditions. First, we give a minimal transmission range that maintains the connectivity of the virtual network constructed from local views. Then, we use two transmission ranges, one for neighborhood information collection and the other for actual data transmission, to form a buffer zone that guarantees the availability of logical links in the physical network. Finally, we propose a mechanism called aggregated local view to ensure consistent local views. By these, we extend Wu and Dai’s coverage condition for broadcasting in a network with mobile nodes. The effectiveness of the proposed scheme is confirmed via both performance analysis and simulation study.

An important problem in wireless ad hoc and sensor networks is to select a few nodes to form a virtual backbone that supports routing and other tasks such as area monitoring. Previous work in this area has focused on selecting a small vir-tual backbone for high efficiency. In this paper, we propose the construction of a k-connected k-dominating set (k-CDS) as a backbone to balance efficiency and fault tolerance. Four localized k-CDS construction protocols are proposed. The first pro-tocol randomly selects virtual backbone nodes with a given probability pk, where pk depends on the value of k and network condition, such as network size and node density. The second one maintains a fixed backbone node degree of Bk, where Bk also depends on the network condition. The third protocol is a deterministic ap-proach. It extends Wu and Dai’s coverage condition, which is originally designed for 1-CDS construction, to ensure the formation of a k-CDS. The last protocol is a hybrid of probabilistic and deterministic approaches. It provides a generic frame-work that can convert many existing CDS algorithms into k-CDS algorithms. These protocols are evaluated via a simulation study. Key words: Connected dominating set (CDS), k-vertex connectivity, localized algorithms, simulation, wireless ad hoc and sensor networks. PACS: Preprint submitted to Elsevier Science 23 September 2005

Abstract — We consider a wireless sensor network con-sisting of a set of sensors deployed randomly. A point in the monitored area is covered if it is within the sensing range of a sensor. In some applications, when the network is sufficiently dense, area coverage can be approximated by guaranteeing point coverage. In this case, all the points of wireless devices could be used to represent the whole area, and the working sensors are supposed to cover all the sensors. Many applications related to security and reliability require guaranteed k-coverage of the area at all times. In this paper, we formalize the k-(Connected) Coverage Set (k-CCS/k-CS) problems, develop a linear programming algorithm, and design two non-global solu-tions for them. Some theoretical analysis is also provided followed by simulation results. Index Terms — Coverage problem, linear programming, localized algorithms, reliability, wireless sensor networks.

Abstract — Multipoint relays (MPR) [1] provides a localized and optimized way of broadcasting messages in a mobile ad hoc network (MANET). Using 2-hop neighborhood information, each node determines a small set of forward neighbors to relay messages. Selected forward nodes form a connected dominating set (CDS) to ensure full coverage. Adjih, Jacquet, and Viennot [2] proposed a novel localized algorithm to construct a small CDS based on the original MPR. In this paper, we provide several extensions to generate a smaller CDS using 3-hop neighborhood information to cover each node’s 2-hop neighbor set. In addition, we extend the notion of coverage in the original MPR. We show that the extended MPR has a constant local approximation ratio compared with a logarithmic local ratio in the original MPR. The effectiveness of our approach is confirmed through a simulation study.

Abstract—Since there is no fixed infrastructure or centralized management in wireless ad hoc networks, a Connected Dominating Set (CDS) has been proposed to serve as a virtual backbone. The CDS of a graph representing a network has a significant impact on the efficient design of routing protocols in wireless networks. This problem has been studied extensively in Unit Disk Graphs (UDG), in which all nodes have the same transmission ranges. However, in practice, the transmission ranges of all nodes are not necessarily equal. In this paper, we model a network as a disk graph and introduce the CDS problem in disk graphs. We present two efficient approximation algorithms to obtain a minimum CDS. The performance ratio of these algorithms is constant if the ratio of the maximum transmission range over the minimum transmission range in the network is bounded. These algorithms can be implemented as distributed algorithms. Furthermore, we show a size relationship between a maximal independent set and a CDS as well as a bound of the maximum number of independent neighbors of a node in disk graphs. The theoretical analysis and simulation results are also presented to verify our approaches. Index Terms—Connected dominating set, independent set, disk graph, wireless network, virtual backbone. 1

We present an algorithm that finds trees with at least k leaves in undirected and directed graphs. These problems are known as Maximum Leaf Spanning Tree for undirected graphs, and, respectively, Directed Maximum Leaf Out-Tree and Directed Maximum Leaf Spanning Out-Tree in the case of directed graphs. The run time of our algorithm is O(poly(|V |) + 4 k k 2) on undirected graphs, and O(4 k |V |·|E|) on directed graphs. Currently, the fastest algorithms for these problems have run times of O(poly(n) + 6.75 k poly(k)) and 2 O(k log k) poly(n), respectively.

A Connected Dominating Set (CDS) working as a virtual backbone is an effective way to decrease the overhead of routing in a wireless sensor network. Furthermore, a k-Connected m-Dominating Set (kmCDS) is necessary for fault tolerance and routing flexibility. Some approximation algorithms have been proposed to construct a kmCDS. However, most of them only consider some special cases where k = 1, 2 or k ≤ m, or are not easy to implement, or have high message complexity. In this paper, we propose a novel distributed algorithm LDA with low message complexity to construct a kmCDS for general k and m whose size is guaranteed to be within a small constant factor of the optimal solution when the maximum node degree is a constant. We also propose one centralized algorithm ICGA with a constant performance ratio to construct a kmCDS. Theoretical analysis as well as simulation results are shown to evaluate the proposed algorithms.

We study local, distributed algorithms for the capacitated minimum dominating set (CapMDS) problem, which arises in various distributed network applications. Given a network graph G = (V, E), and a capacity cap(v) ∈ N for each node v ∈ V, the CapMDS problem asks for a subset S ⊆ V of minimal cardinality, such that every network node not in S is covered by at least one neighbor in S, and every node v ∈ S covers at most cap(v) of its neighbors. We prove that in general graphs and even with uniform capacities, the problem is inherently non-local, i.e., every distributed algorithm achieving a non-trivial approximation ratio must have a time complexity that essentially grows linearly with the network diameter. On the other hand, if for some parameter ɛ> 0, capacities can be violated by a factor of 1 + ɛ, CapMDS becomes much more local. Particularly, based on a novel distributed randomized rounding technique, we present a distributed bi-criteria algorithm that achieves an O(log ∆)-approximation in time O(log 3 n + log(n)/ɛ), where n and ∆ denote the number of nodes and the maximal degree in G, respectively. Finally, we prove that in geometric network graphs typically arising in wireless settings, the uniform problem can be approximated within a constant factor in logarithmic time, whereas the non-uniform problem remains entirely non-local.

Abstract. We propose a new Connected Dominating Set (CDS) based algorithm for clustering in Mobile Ad hoc Networks (MANETs). Our algorithm is based on Wu and Li’s [14] algorithm, however we provide significant modifications by considering the degrees of the nodes during marking process and also provide further heuristics to determine the color of a node in the initial phase. We describe, analyze and measure performance of this new algorithm by simulation and show that it performs better than Wu and Li’s [14] algorithm especially in the case of dense networks. 1

Using directional antennas to conserve bandwidth and energy consumption in ad hoc wireless networks (or simply ad hoc networks) is becoming popular in recent years. However, applications of directional antennas for broadcasting have been limited. We propose a novel broadcast protocol called directional self-pruning (DSP) for ad hoc wireless networks using directional antennas. DSP is a nontrivial generalization of an existing localized deterministic broadcast protocol using omnidirectional antennas. Compared with its omnidirectional predecessor, DSP uses about the same number of forward nodes to relay the broadcast packet, while the number of forward directions that each forward node uses in transmission is significantly reduced. With the lower broadcast redundancy, DSP is more bandwidth and energy-efficient. DSP is based on 2-hop neighborhood information and does not rely on location or angle-ofarrival (AoA) information. Two special cases of DSP are discussed: the first one preserves shortest paths in reactive routing discoveries; the second one uses the directional reception mode to minimize broadcast redundancy. DSP is a localized protocol. Its expected number of forward nodes is Oð1Þ times the optimal value. An extensive simulation study using both custom and ns2 simulators shows that DSP significantly outperforms both omnidirectional broadcast protocols and existing directional broadcast protocols.