The Most Likely Object to be Seen Through a Window

We study data structures to answer window queries using stochastic input sequences. The first problem is the most likely maximal point in a query window: Let [Formula: see text] be constants, with [Formula: see text]. Let [Formula: see text] be a set of [Formula: see text] points in [Formula: see text], for some fixed [Formula: see text]. For [Formula: see text], each point in [Formula: see text] is associated with a probability [Formula: see text] of existence. A point [Formula: see text] in [Formula: see text] is on the maximal layer of [Formula: see text] if there is no other point [Formula: see text] in [Formula: see text] such that [Formula: see text]. Consider a random subset of [Formula: see text] obtained by including, for [Formula: see text], each point of [Formula: see text] independently with probability [Formula: see text]. For a query interval [Formula: see text], with [Formula: see text], we report the point in [Formula: see text] that has the highest probability to be on the maximal layer of [Formula: see text] in [Formula: see text] time using [Formula: see text] space. We solve a special problem as follows. A sequence [Formula: see text] of [Formula: see text] points in [Formula: see text] is given ([Formula: see text]), where each point [Formula: see text] has a probability [Formula: see text] of existence associated with it. Given a query interval [Formula: see text] and an integer [Formula: see text] with [Formula: see text], we report the probability of [Formula: see text] to be on the maximal layer of [Formula: see text] in [Formula: see text] time using [Formula: see text] space. The second problem we consider is the most likely common element problem. Let [Formula: see text] be the universe. Let [Formula: see text] be a sequence of random subsets of [Formula: see text] such that for [Formula: see text] and [Formula: see text], element [Formula: see text] is added to [Formula: see text] with probability [Formula: see text] (independently of other choices). Let [Formula: see text] be a fixed real number with [Formula: see text]. For query indices [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], with [Formula: see text] and [Formula: see text], we decide whether there exists an element [Formula: see text] with [Formula: see text] such that [Formula: see text] in [Formula: see text] time using [Formula: see text] space and report these elements in [Formula: see text] time, where [Formula: see text] is the size of the output.

Neighbor-Index Method for Continuous Window Queries over Wireless Data Broadcast

A continuous window query is an important class of spatial queries for location-based services. It retrieves spatial objects in a fixed window region of every point on a line segment and indicates the valid segments of them. In this paper, we focus on continuous window queries in wireless data broadcast systems. Since the query result of the continuous window queries has the spatial locality, providing neighbor information of spatial objects can guide clients to efficiently retrieve related objects. Therefore, we propose a neighbor-index method to efficiently support the continuous window queries in wireless data broadcast systems. The proposed method interleaves the neighbor information between spatial objects to guide mobile clients to quickly retrieve the answered objects and save the power consumption of the mobile devices. Experimental results show that our method outperforms the distributed indexing.

Enhanced Approaches for Processing Window Queries in Dynamic Wireless Sensor Networks

Due to the proliferation of low cost wireless sensors, there is growing research interest in their applications, for example, in home healthcare and location tracking. However, due to sensors’ energy resource constraint, some possible applications of sensors have been restricted. In particular, in applications concerning deployment of mobile sensors in dynamic environments, high amounts of energy are consumed by sensors to maintain routing tables. Although existing methods have been proposed to query data from sensors without the use of any routing tables, these methods typically require redundant data to be sent back to the sink and not all of the aggregation functions could be executed precisely. In this paper, we modify an existing method to provide more accurate query answers and extend the lifetime of a wireless sensor network (WSN). According to our simulation, this method outperforms the existing method our approach modifies.