A wireless network consisting of a large number of small sensors with low-power transceivers can be an effective tool for gathering data in a variety of environments. The data collected by each sensor is communicated through the network to a single processing center that uses all reported data to determine characteristics of the environment or detect an event. The communication or message passing process must be designed to conserve the Hmited energy resources of the sensors. Clustering sensors into groups, so that sensors communicate information only to clusterheads and then the clusterheads communicate the aggregated information to the processing center, may save energy. In this paper, we propose a distributed, randomized clustering algorithm to organize the sensors in a wireless sensor network into clusters. We then extend this algorithm to generate a hierarchy of clusterheads and observe that the energy savings increase with the number of levels in the hierarchy. Results in stochastic geometry are used to derive solutions for the values of parameters of our algorithm that minimize the total energy spent in the network when all sensors report data through the clusterheads to the processing center.

this paper, we propose an on-demand distributed clustering algorithm for multi-hop packet radio networks. These types of networks, also known as ad hoc networks, are dynamic in nature due to the mobility of the nodes. The association and dissociation of nodes to and from clusters perturb the stability of the network topology, and hence a reconguration of the system is often unavoidable. However, it is vital to keep the topology stable as long as possible. The clusterheads, form a dominant set in the network, determine the topology and its stability. The proposed weight-based distributed clustering algorithm takes into consideration the ideal degree, transmission power, mobility, and battery power of mobile nodes. The time required to identify the clusterheads depends on the diameter of the underlying graph. We try to keep the number of nodes in a cluster around a pre-dened threshold to facilitate the optimal o

Abstract—We consider a heterogeneous sensor network in which nodes are to be deployed over a unit area for the purpose of surveillance. An aircraft visits the area periodically and gathers data about the activity in the area from the sensor nodes. There are two types of nodes that are distributed over the area using two-dimensional homogeneous Poisson point processes; type 0 nodes with intensity (average number per unit area) 0 and battery energy E0; and type 1 nodes with intensity 1 and battery energy E1. Type 0 nodes do the sensing while type 1 nodes act as the cluster heads besides doing the sensing. Nodes use multihopping to communicate with their closest cluster heads. We determine the optimum node intensities ( 0, 1) and node energies (E0, E1) that guarantee a lifetime of at least T units, while ensuring connectivity and coverage of the surveillance area with a high probability. We minimize the overall cost of the network under these constraints. Lifetime is defined as the number of successful data gathering trips (or cycles) that are possible until connectivity and/or coverage are lost. Conditions for a sharp cutoff are also taken into account, i.e., we ensure that almost all the nodes run out of energy at about the same time so that there is very little energy waste due to residual energy. We compare the results for random deployment with those of a grid deployment in which nodes are placed deterministically along grid p ffiffiffiffiffi points. We observe that in both cases 1 scales approximately as 0. Our results can be directly extended to take into account unreliable nodes. Index Terms—Sensor networks, energy, lifetime, stochastic geometry, Voronoi cells. 1

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.

A connected dominating set in a graph is a subset of vertices such that every vertex is either in the subset or adjacent to a vertex in the subset and the subgraph induced by the subset is connected. The minimum connected dominating set is such a vertex subset with minimum cardinality. An application in ad hoc wireless networks requires the study of the minimum connected dominating set in unit-disk graphs. In this paper, we design (1+1=s)-approximation for the minimum connected dominating set in unit-disk graphs, running in time n O((slogs) 2 )

supported by NSF CCR-0311174. Abstract — Topology control has been well studied in wireless ad hoc networks. However, only a few topology control methods take into account the low interference as a goal of the methods. Some researchers tried to reduce the interference by lowering node energy consumption (i.e. by reducing the transmission power) or by devising low degree topology controls, but none of those protocols can guarantee low interference. Recently, Burkhart et al. [?] proposed several methods to construct topologies whose maximum link interference is minimized while the topology is connected or is a spanner for Euclidean length. In this paper we give algorithms to construct a network topology for wireless ad hoc network such that the maximum (or average) link (or node) interference of the topology is either minimized or approximately minimized. Index Terms — Topology control, interference, wireless ad hoc networks.

The efficiency of a communication network depends not only on its control protocols, but also on its topology. We propose a distributed topology management algorithm that constructs and maintains a backbone topology based on a minimal dominating set (MDS) of the network. According to this algorithm, each node determines the membership in the MDS for itself and its one-hop neighbors based on two-hop neighbor information that is disseminated among neighboring nodes. The algorithm then ensures that the members of the MDS are connected into a connected dominating set (CDS), which can be used to form the backbone infrastructure of the communication network for such purposes as routing. The correctness of the algorithm is proven, and the efficiency is compared with other topology management heuristics using simulations. Our algorithm shows better behavior and higher stability in ad hoc networks than prior algorithms.

Ad hoc networks consist of wireless hosts that communicate with each other in the absence of a fixed infrastructure. Clustering is commonly used in order to limit the amount of routing information stored and maintained at individual hosts. A k-clustering is a framework in which the wireless network is divided into non-overlapping sub networks, also referred to as clusters, and where every two wireless hosts in a sub network are at most k hops from each other. The algorithmic complexity of k-clustering is known to be NP-Complete for simple undirected graphs. For the special family of graphs that represent ad hoc wireless networks, modeled as unit disk graphs, we introduce a two phase distributed polynomial time and message complexity approximation solution with O(k) worst case ratio over the optimal solution. The first phase constructs a spanning tree of the network and the second phase then partitions the spanning tree into subtrees with bounded diameters.

We present an overview of the recent progress of applying computational geometry techniques to solve some questions, such as topology construction and broadcasting, in wireless ad hoc networks. Treating each wireless device as a node in a two dimensional plane, we model the wireless networks by unit disk graphs in which two nodes are connected if their Euclidean distance is no more than one. We rst summarize the current status of constructing sparse spanners for unit disk graphs with various combinations of the following properties: bounded stretch factor, bounded node degree, planar, and bounded total edges weight (compared with the minimum spanning tree). Instead of constructing subgraphs by removing links, we then review the algorithms for constructing a sparse backbone (connected dominating set), i.e., subgraph from the subset of nodes. We then review some ecient methods for broadcasting and multicasting with theoretic guaranteed performance.

Ad hoc wireless network is featured by dynamic topology. There is no fixed infrastructure as compared with wired network. Every host can move to any direction at any speed. This characteristic puts special challenges in routing protocol design.