Khaled M. Alzoubi

Message-optimal connected dominating sets in mobile ad hoc networks

A connected dominating set (CDS) for a graph G(V,E) is a subset V1 of V, such that each node in V--V1 is adjacent to some node in V1, and V1 induces a connected subgraph. A CDS has been proposed as a virtual backbone for routing in wireless ad hoc networks. However, it is NP-hard to find a minimum connected dominating set (MCDS). Approximation algorithms for MCDS have been proposed in the literature. Most of these algorithms suffer from a very poor approximation ratio, and from high time complexity and message complexity. Recently, new distributed heuristics for constructing a CDS were developed, with constant approximation ratio of 8. These new heuristics are based on a construction of a spanning tree, which makes it very costly in terms of communication overhead to maintain the CDS in the case of mobility and topology changes.In this paper, we propose the first distributed approximation algorithm to construct a MCDS for the unit-disk-graph with a emph constant approximation ratio, and emph linear time and emph linear message complexity. This algorithm is fully localized, and does not depend on the spanning tree. Thus, the maintenance of the CDS after changes of topology guarantees the maintenance of the same approximation ratio. In this algorithm each node requires knowledge of its single-hop neighbors, and only a constant number of two-hop and three-hop neighbors. The message length is O( log n) bits.

New distributed algorithm for connected dominating set in wireless ad hoc networks

Connected dominating set (CDs) has been proposed as virtual backbone or spine of wireless ad hoc networks. Three distributed approximation algorithms have been proposed in the literature for minimum CDS. We first reinvestigate their performances. None of these algorithms have constant approximation factors. Thus these algorithms can not guarantee to generate a CDs of small size. Their message complexities can be as high as O(n/sup 2/), and their time complexities may also be as large as O(n/sup 2/) and O(n/sup 3/). We then present our own distributed algorithm that outperforms the existing algorithms. This algorithm has an approximation factor of at most 8, O(n) time complexity and O(n log n) message complexity. By establishing the /spl Omega/(n log n) lower bound on the message complexity of any distributed algorithm for nontrivial CDs, our algorithm is thus message-optimal.

Distributed construction of connected dominating set in wireless ad hoc networks

Connected dominating set (CDS) has been proposed as virtual backbone or spine of wireless ad hoc networks. Three distributed approximation algorithms have been proposed in the literature for minimum CDS. In this paper, we first reinvestigate their performances. None of these algorithms have constant approximation factors. Thus these algorithms cannot guarantee to generate a CDS of small size. Their message complexities can be as high as O(n2), and their time complexities may also be as large as O(n2) and O(n3). We then present our own distributed algorithm that outperforms the existing algorithms. This algorithm has an approximation factor of at most 8, O(n) time complexity and O(nlog n) message complexity. By establishing the Ω(nlog n) lower bound on the message complexity of any distributed algorithm for nontrivial CDS, our algorithm is thus message-optimal.

Geometric spanners for wireless ad hoc networks

We propose a new geometric spanner for static wireless ad hoc networks, which can be constructed efficiently in a localized manner. It integrates the connected dominating set and the local Delaunay graph to form a backbone of the wireless network. Priori arts showed that both structures can be constructed locally with bounded communication costs. This new spanner has these following attractive properties: 1) the backbone is a planar graph, 2) the node degree of the backbone is bounded from above by a positive constant, 3) it is a spanner for both hops and length, 4) it can be constructed locally and is easy to maintain when the nodes move around, and 5) moreover, the communication cost of each node is bounded by a constant. Simulation results are also presented for studying its practical performance.

MAXIMAL INDEPENDENT SET, WEAKLY-CONNECTED DOMINATING SET, AND INDUCED SPANNERS IN WIRELESS AD HOC NETWORKS

A maximal independent set (MIS) S for a graph G is an independent set and no proper superset of S is also independent. A set S is dominating if each node in the graph is either in S or adjacent to one of the nodes in S. The subgraph weakly induced by S is the graph G′ such that each edge in G′ has at least one end point in S. A set S is a weakly-connected dominating set (WCDS) of G if S is dominating and G′ is connected. G′ is a sparse spanner if it has linear edges. The nodes of WCDS have been proposed in the literature as clusterheads for clustered wireless ad hoc networks. In this paper, we present two distributed algorithms for constructing a WCDS for wireless ad hoc networks in linear time. The first algorithm has an approximation ratio of 5, and requires O(n log n) messages, while the second algorithm has a larger approximation ratio, and requires only O(n) messages. Both of these algorithms are used to obtain sparse spanners. The spanner obtained by the second algorithm has a topological dilation of 3, and a geometric dilation of 6. Both of these algorithms are based on the construction of a MIS. The first algorithm requires the construction of a spanning tree. The second algorithm is fully localized, and does not depend on the spanning tree, which makes the maintenance of the WCDS simpler, and guarantees the maintenance of the same approximation ratio.

A SIMPLE HEURISTIC FOR MINIMUM CONNECTED DOMINATING SET IN GRAPHS

Let α2(G), γ(G) and γc(G) be the 2-independence number, the domination number, and the connected domination number of a graph G respectively. Then α2(G) ≤ γ (G) ≤ γc(G). In this paper , we present a simple heuristic for Minimum Connected Dominating Set in graphs. When running on a graph G excluding Km (the complete graph of order m) as a minor, the heuristic produces a connected dominating set of cardinality at most 7α2(G) - 4 if m = 3, or at most if m ≥ 4. In particular, if running on a planar graph G, the heuristic outputs a connected dominating set of cardinality at most 15α2(G) - 5.

Robust quality of service backbone for mobile ad hoc networks

Mobile ad hoc networks (MANETs) are a rapidly growing field today. Unlike conventional wireless networks, MANETs have no physical backbone infrastructure and no administrative support. Generally, these networks are characterized by scarce resources (e.g. bandwidth, power, etc.), high error rates, and a dynamic topology. In MANETs, the quality of service (QoS) aspect, in general, and QoS routing, in particular, need more attention as a result of the rising popularity and necessity- of real-time multimedia applications. Currently, no robust QoS backbone algorithm can efficiently serve a MANET environ. This paper proposes a novel QoS backbone construction algorithm for MANETs. The backbone nodes are mainly selected based on individual node stability and available bandwidth for each node. Then, these nodes are implicitly connected using link bandwidth and delay as QoS metrics. The proposed algorithm, its performance analysis, and simulation results are presented in this paper

An Entity Stability Measure for Mobile Ad Hoc Networks

Due to the built-in mobility nature of mobile ad hoc networks (MANETs), the network topology constantly changes. Consequently, the state information for routing processes is imprecise. Examples of state information that are directly impacted by mobility are: delay, bandwidth, error rates, and jitter. The effect of mobility on the state information is critical to the extent that makes the QoS routing problem extremely complicated and inherently challenging. In this paper we provide an analytical estimation of an entity node stability measure (s n). This measure is a new preemptive stability measure that relies on predicting the lifetime of the links