## Retrieval of the Extreme Values under Deadline Constraints in Wireless Sensor Networks  
**[PERSON] \({}^{1,\star}\), [PERSON] \({}^{1}\), [PERSON] \({}^{2}\) and [PERSON] \({}^{3}\)**  
\({}^{1}\) Department of Computer and Communications, Korea University, Anam-dong Seongbuk-gu,  
130-701, Seoul, Korea; E-Mail: [EMAIL_ADDRESS]  
\({}^{2}\) Department of Digital Contents Convergence, Seoul National University, Seoul, Korea;  
E-Mail: [EMAIL_ADDRESS]  
\({}^{3}\) Electronics and Telecommunications Research Institute, 138 Gajeongno, Yuseong-gu, Daejeon,  
305-700, Korea; E-Mail: [EMAIL_ADDRESS]  
\({}^{\star}\) Author to whom correspondence should be addressed; E-Mail: [EMAIL_ADDRESS];  
Tel. : +82-2-3290-4847. Received: 20 April 2011; in revised form: 2 May 2011 / Accepted: 11 May 2011 /  
Published: 12 May 2011  
**Abstract:** We consider a problem of retrieving the extreme value among sensed data under deadline constraints in wireless sensor networks with potential applications to alarm systems. The sensed data is mapped to a score which we adopt as a unified measure of the relative urgency of the data. The objective is to retrieve the data with the maximum score. We propose fully distributed schemes for contention based medium access and data combining. The proposed medium access scheme uses a randomized back-off which is controlled based on the score of the data to be transmitted. Data combining techniques are proposed to further suppress unnecessary traffic and reduce contention. The key observation is that one should aggressively prioritize packets with high score, up to an extent that does not incur excessive contention in channel access. Designed to capture such aspect, the proposed scheme is shown to substantially decrease the latency of the retrieval. **Keywords:** wireless sensor networks; medium access control; distributed algorithm; latency Introduction  
Wireless sensor networks (WSN) are networks of battery-operated sensors which are capable of wireless communication. WSNs envision a wide range of applications in environmental and habitat monitoring, military surveillance, building and facility monitoring, and emergency medical care. An important property of WSNs is that they are application-centric, _i.e._, WSNs are deployed to carry out a specific mission. Thus it is desirable that the design of WSN is adapted to specific tasks so as to optimize the performance in mission execution. Commonly an objective of WSNs is to provide a _summary_ of the sensed data generated in the network. The relevant summary is defined as certain function applied to the raw sensor data [1]. Given the sensor readings \(x_{1},x_{2},\ldots,x_{n}\), the goal is to compute \(f(x_{1},x_{2},\ldots,x_{n})\). Examples of \(f(\cdot)\) are mean, max, min, _etc._ When mean function is used, \(f(x_{1},\ldots,x_{n})=\sum_{i=1}^{n}x_{i}/n\). In this paper we study the design of WSN with an objective of _extreme_ data retrieval. Specifically \(f(\cdot)\) of interest is max or min, however these two objectives are identical in nature, thus without loss of generality we will focus on max. Note WSNs for such extreme data retrieval is suitable for 'alarm' systems [1]. For example suppose \(f(x_{1},\ldots,x_{n})=\max_{i=1,\ldots,n}\left[x_{i}\right]\) where \(x_{i}\) are the temperature values of the monitoring region. Then the mission can be to identify the highest temperature value and its location so that an alarm is triggered if the value is above a threshold. A crucial aspect of emergency applications is to retrieve the information in a timely manner. We assume that there is a strict deadline for data retrieval, and we focus on maximizing the probability of the retrieval of the extreme data at the deadline. When the data samples \(x_{1},x_{2},\ldots,x_{n}\) are drawn from random variables (RV) \(X_{1},X_{2},\ldots,X_{n}\) with _different_ distributions, it is meaningless to directly compare the values \(x_{1},\ldots,x_{n}\) or to compute max among the data.