1 Energy-Efficient Routing Schemes for Wireless Sensor Networks Maleq Khan Gopal Pandurangan Bharat Bhargava Abstract— Microsensors operate under severe energy constraints. Depending on the application, sensors can be thrown randomly in an area of interest (“sprinkled in a field”) or, in some cases, can be manually placed in specific positions. The sensor network is typically ad hoc, formed by local self-configuration. Data-centric routing is a new use- ful paradigm for energy-constrained sensor networks. The data coming from different sources are aggregated at the intermediate nodes on the way; that reduces volume of data (eliminating redundancy) and saves transmission energy. In this paper, we design and analyze optimal network config- urations and data-centric routing schemes to minimize en- ergy consumption for both random and manual placement of nodes. Specifically, the paper makes the following con- tributions. We first study energy-optimal network configu- rations for manual and random placement of nodes under a natural coverage criterion. In particular, we show that in a linear network, energy consumption is minimal when nodes are equally spaced. For a two dimensional network, energy consumptions for various manual uniform arrange- ments such as triangular, square, and hexagonal array of sensors are analyzed and compared. We also rigorously an- alyze expected energy consumption under random distribu- tion. We then show that a minimal spanning tree (MST) is the optimal data aggregation tree for energy-efficient rout- ing. We then study energy-efficient distributed algorithms for constructing MSTs. The GHS algorithm to construct MST has an optimal message complexity, but can be energy- expensive. A key contribution of the paper is a new simple algorithm called the Nearest Neighbor Tree (NNT) to build slightly sub-optimal trees, but is very energy-efficient com- pared to the GHS algorithm. Simulation results shows that NNT gives a close approximation to MST and consumes much less energy compared to GHS in constructing the tree. Index Terms—Graph theory, Stochastic processes, Opti- mization, Sensor networks, Data-centric routing. I. I NTRODUCTION AND OVERVIEW Advances in integrated circuit technology have en- abled mass production of tiny, cost-effective, and energy- efficient wireless sensor devices with on-board process- ing capabilities. The emergence of mobile and pervasive computing has created new applications for them. Sensor- based applications span a wide range of areas, including This research was partially supported by CERIAS, and NSF Grants ANI-0219110 and CCR-001712. The authors are at the Department of Computer Sciences, Purdue University, West Lafayette, IN 47907. Email: {mmkhan, gopal, bb}@cs.purdue.edu. remote monitoring of seismic activities, environmental factors (e.g., air, water, soil, wind, chemicals), condition- based maintenance, smart spaces, military surveillance, precision agriculture, transportation, factory instrumenta- tion, and inventory tracking [1], [2]. A. Sensor Networks A microsensor is a device which is equipped with a sen- sor module (e.g., an acoustic, a seismic, or an image sen- sor) capable of sensing some entity in the environment, a digital unit for processing the signals from the sensors and performing network protocol functions, a radio mod- ule for communication, and a battery to provide energy for its operation [2]. Microsensors typically have low pro- cessing power and slow communication ability. For ex- ample, Berkeley mote [3] has a 8-bit Atmel AT90LS8535 microcontroller running at 4 MHz. A low-power radio transceiver MICA2, designed for sensor networks, oper- ates at 916 MHz and provides a data transmission rate of 19.2 Kbps [4]. These parameters ensure limited weight, size, and cost. The size of a MICA2 MPR400CB is 2.25 ′′ × 1.2 ′′ × 0.25 ′′ . We use the term sensor to refer to a microsensor. Networking of the sensors, when deployed in large numbers and embedded deeply within large-scale physi- cal systems, enables to measure aspects of the physical environment in unprecedented detail [1]. There are some similarities between wireless sensor networks and wire- less ad-hoc networks. One of the similar characteristics for both of them is multi-hop communications. Some of the power-aware routing protocols [5], [6], [7], [8] pro- posed for wireless ad-hoc networks can be examined in the context of wireless sensor networks with stringent en- ergy constraints. However, these protocols may not be efficient, effective or feasible, in sensor networks. The nature of applications and routing requirements for the two are significantly different in several aspects [9]. First, the typical mode of communication in a sensor network is from multiple data sources to a data recipient/sink rather than communication between any pair of nodes. Second, since the data being collected by multiple sensors is based on common phenomena, there is likely to be some re- dundancy in the data being communicated by the various sources in sensor networks. Third, in most envisioned sce- narios the sensors are not mobile, so the nature of the dy- namics in the two networks is different. Finally, the single