【正文】 e work considered by them is inter style and consists of nodes with ample putational power, which is very different from the energylimited wireless sensor works we consider. In wireless sensor works, the notion of inwork processing was first introduced by Intanagonwiwat et al. [18] to opportunistically eliminate duplicates in the context of directed diffusion. Gehrke and Madden et al.[11,15,24] are among the first to integrate query processing and sensor works so tasking sensor works can be easily done through declarative queries. In the Cougar project [11], a layered architecture of sensor data management is proposed for presenting the sensor work as a distributed database system. In TinyDB [24], a framework Of query processing in WSN is introduced for addressing issues of when, where, and how often data is sampled and which data is delivered in wireless sensor works. Energy efficiency is one of the major factors considered in [11,24], but not with the goal of maximizing the system lifetime. In addition, query operators in [11,24] are modeled from a functionality perspective and often are rather simple operators (aggregation, filter, etc.), while in our work we model the operators from a munication perspective with the consideration of their optimal placement . Ren et al .[27] consider quality aware processing of simple aggregate queries (. pute the average, min, max of measurements of sensors in a rectangular area of interest). A centralized algorithm is proposed to find a subset of sensors whose measurements are collected using reactive routing to the base station to pute a probabilistic answer. Hu et al. [17], expanding upon the work of Olston and Widom[25],are concerned with approximate answers to continuous aggregate queries (sum, mean, count, etc.). They provide a method to allocate a userspecified acceptable tolerance to a query’s answer as tolerance ranges for the sensors. Subsequently, a sensor sends its measurement to the base station if it falls outside its tolerance range. These two works are different from ours in many respects: we consider plex queries with various operators besides min, max, avg, we provide accurate answers to queries, and we seek to optimize the system lifetime directly. Many researchers have advocated the use of datacentric techniques that allow for efficient inwork storage and retrieval of named data using queries [16]. A number of datacentric pushpull query processing techniques have been proposed and examined [6,8,23,28,29,31], which can be categorized to two main approaches: structured and unstructured, which can be represented by the geographic hashbased datacentric storage technique [29] and the bneedle method [23] respectively. Kapadia and Krishnamachari [20] present a parative mathematical analysis of these two approaches based on two types of simple oneshot queries (ALLtype and ANYtype) in singlesink squaregrid sensor works, and later on, Ahn and Krishnamachari [2] find that the scalability of a datacentric sensor works performance depends upon whether or not the increase in energy and storage resources with more nodes is outweighed by the resulting applicationspecific increase in event and query loads. Bonfils et al. [5] consider the placement of operators of a query expression tree to the nodes of a sensor work to minimize the total munication cost of evaluating such a tree. For any pair of parentchild operators in the query tree, the induced munication cost is the product of the length of a shortest path between the nodes, where these operators are placed and the data rate from the child to its parent. They provide a distributed protocol that attempts to refine the placement by continuously walking through neighbor nodes to acmodate the data rate change . The overhead of message exchange generated by walking through neighbor nodes is not considered in [5]. Our ALGRSMMLCF algorithm differs from theirs in that we allow data to be routed over multiple paths rather than as ingle path, and that we seek to optimize the system lifetime rather than the total munication cost. Restricting routing of childparent data to a single path instead of allowing multiple paths can have a detrimental effect on the lifetime. As can been seen in Fig. 10, our approach achieves much better lifetime in all the instances over the best placement when using shortest path routing. Srivastava et al. [30] consider the problem of placing operators onto a hierarchy of work nodes with progressively increasing putational power and work bandwidth, such that the total cost of putation and munication is minimized. We assume a different work model in which sensors are homogeneous and are energy limited, and a different goal of optimizing the system lifetime, which does not necessarily result from minimizing the total cost of putation and munication. Garg and Konemann [14] describe an iterative algorithm with provable approximation ratio for solving the maximum concurrent multimodity flow problem ,Whose LP formulation is different from MLCF . Their objective is to maximize the total work flow under limited capacity of edges, while ours is to maximize work lifetime under limited energy of nodes. In addition, the number of routing paths used in the solution of our ALGRSMMLCF algorithm is bounded, while the algorithm in [14] finds solutions which may use as many routing path as the number of iterations. Having fewer routing paths is important in practice, since the overhead of distributing the relevant routing information to the sensors is kept smaller with fewer paths. Chang and Tassiulas