Topology control in a sensor network balances load on sensor nodes, and increases network scalability and lifetime. Clustering sensor nodes is an effective topology control approach. In this paper, we propose a novel distributed clustering approach for long-lived ad-hoc sensor networks. Our proposed approach does not make any assumptions about the presence of infrastructure or about node capabilities, other than the availability of multiple power levels in sensor nodes. We present a protocol, HEED (Hybrid Energy-Efficient Distributed clustering), that periodically selects cluster heads according to a hybrid of the node residual energy and a secondary parameter, such as node proximity to its neighbors or node degree. HEED terminates in O(1) iterations, incurs low message overhead, and achieves fairly uniform cluster head distribution across the network. We prove that, with appropriate bounds on node density and intra-cluster and inter-cluster transmission ranges, HEED can asymptotically almost surely guarantee connectivity of clustered networks. Simulation results demonstrate that our proposed approach is effective in prolonging the network lifetime and supporting scalable data aggregation.

To achieve security in wireless sensor networks, it is important to be able to encrypt messages sent among sensor nodes. Keys for encryption purposes must be agreed upon by communicating nodes. Due to resource constraints, achieving such key agreement in wireless sensor networks is non-trivial. Many key agreement schemes used in general networks, such as Diffie-Hellman and public-key based schemes, are not suitable for wireless sensor networks. Pre-distribution of secret keys for all pairs of nodes is not viable due to the large amount of memory used when the network size is large. Recently, a random key predistribution scheme and its improvements have been proposed.

Spatial query execution is an essential functionality of a sensor network, where a query gathers sensor data within a specific geographic region. Redundancy within a sensor network can be exploited to rv uce the communication cost incurv1 in execution of such quer ies. Anyr eduction in communication cost wouldr esult in an e#cient use of the batter y ener gy, which is ver y limited in sensor s. One appr oach to r educe the communication cost of a quer y is to self-or ganize the networ# inr esponse to a quer , into a topology that involves only a small subset of the sensor s su#cient to pr ocess the quer y. The quer y is then executed using only the sensor in the constr ucted topology. In thisar icle, we design and analyze algor thms for such self-or"/0 zation of asensor networ tor educe enerP consumption. In par icular we develop the notion of a connected sensor cover and design a centr alized appr oximation algor thm that constr ucts a topology in ol ing anear optimal connected sensor co er . We pr o e that the size of the const rst ed topology is within an O(log n)factor ofthe optimal size, wher n is the networ size. We also de elop a distr ibuted self-or$1" zationer" on ofour algor thm, and prv ose seer/ optimizations tor educe the communication oer"E1 of the algorithm. Finally, we evaluate the distributed algorithm using simulations and show that our approach results in significant communication cost reduction.

This paper investigates the problem of providing network coverage using wireless sensors that operate on low duty cycles (measured by the percentage time a sensor is on or active), i.e., each sensor alternates between active and sleep states to conserve energy with an average sleep period (much) longer than the active period. The dynamic change in topology as a result of such duty-cycling has potentially disruptive effect on the operation and performance of the network. This is compensated by adding redundancy in the sensor deployment. In this paper we examine the fundamental relationship between the reduction in sensor duty cycle and the required level of redundancy for a fixed performance measure, and explore the design of good sensor sleep schedules. In particular, we consider two types of mechanisms, the random sleep type where each sensor keeps an active-sleep schedule independent of another, and the coordinated sleep type where sensors coordinate with each other in reaching an active-sleep schedule. Both types are studied within the context of providing network coverage. We present specific scheduling algorithms within each type, and illustrate their coverage and duty cycle properties via both analysis and simulation. We show with either type of sleep schedule the benefit of added redundancy saturates at some point in that the reduction in duty cycles starts to diminish beyond a certain threshold in deployment redundancy. We also show that at the expense of extra control overhead, a coordinated sleep schedule is more robust and can achieve higher duty cycle reduction with the same amount of redundancy compared to a random sleep schedule.

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

Previous work on the coverage of mobile sensor networks focuses on algorithms to reposition sensors in order to achieve a static configuration with an enlarged covered area. In this paper, we study the dynamic aspects of the coverage of a mobile sensor network that depend on the process of sensor movement. As time goes by, a position is more likely to be covered; targets that might never be detected in a stationary sensor network can now be detected by moving sensors. We characterize the area coverage at specific time instants and during time intervals, as well as the time it takes to detect a randomly located stationary target. Our results show that sensor mobility can be exploited to compensate for the lack of sensors and improve network coverage. For mobile targets, we take a game theoretic approach and derive optimal mobility strategies for sensors and targets from their own perspectives.

We study the connectivity and capacity of finite area ad hoc wireless networks, with an increasing number of nodes (dense networks). We find that the properties of the network strongly depend on the shape of the attenuation function. For power law attenuation functions, connectivity scales, and the available rate per node is known to decrease like 1/ # n.Onthe contrary, if the attenuation function does not have a singularity at the origin and is uniformly bounded, we obtain bounds on the percolation domain for large node densities, which show that either the network becomes disconnected, or the available rate per node decreases like 1/n.

one approach to conserve energy is to keep only a small subset of sensors active at any instant. In this article, we consider the problem of selecting a minimum size connected-cover, which is defined as a set of ¡ sensors such that each point in the sensor network is “covered” by at least

Abstract. Random geometric graphs result from taking n uniformly distributed points in the unit cube, [0, 1] d, and connecting two points if their Euclidean distance is at most r, for some prescribed r. We show that monotone properties for this class of graphs have sharp thresholds by reducing the problem to bounding the bottleneck matching on two sets of n points distributed uniformly in [0, 1] d. We present upper bounds on the threshold width, and show that our bound is sharp for d = 1 and at most a sublogarithmic factor away for d ≥ 2. Interestingly, the threshold width is much sharper for random geometric graphs than for Bernoulli random graphs. Further, a random geometric graph is shown to be a subgraph, with high probability, of another independently drawn random geometric graph with a slightly larger radius; this property is shown to have no analogue for Bernoulli random graphs. 1.

We consider the problem of a user querying for information over a sensor network, where the user does not have prior knowledge of the location of the information. We consider three information query strategies: (i) a Source-only search, where the source (user) tries to locate the destination by initiating query which propagates as a continuous time random walk (Brownian motion); (ii) a Source and Receiver Driven “Sticky ” Search, where both the source and the destination send a query or an advertisement, and these leave a “sticky ” trail to aid in locating the destination; and (iii) where the destination information is spatially cached (i.e., repeated over space), and the source tries to locate any one of the caches. After a random interval of time with average t, if the information is not located, the query times-out, and the search is unsuccessful. For a source-only search, we show that the probability that a query is unsuccessful decays as (log(t)) −1. When both the source and the destination send queries or advertisements, we show that the probability that a query is unsuccessful decays as t −5/8. Further, faster polynomial decay rates can be achieved by using a finite number of queries or advertisements. Finally, when a spatially periodic cache is employed, we show that the probability that a query is unsuccessful