The multidimensional similarity query, an essential query for information processing in sensor networks, has not received sufficient attention in the research community of sensor networks. In this paper, we study the multidimensional similarity query for large-scale sensor networks and propose a new algorithm called DIC (dimension reduction by Chebyshev polynomials). In DIC algorithm, the normalized Chebyshv coefficients are adopted as indexing and theoretic storage location of multidimensional data, and the multidimensional data are stored in the sensor nodes close to the theoretic location. A query bounding is estimated by using DIC algorithm, and query is executed inside a small zone. Inside the small zone, a new method of the itinerary-based query propagation and data aggregation is presented. The DIC algorithm does not require to preserve any index structure in sensor nodes, and also do not reply on any infrastructure structures distributed among the sensor nodes. We provide extensive experiments to evaluate the performance of the algorithm. The experimental results demonstrate that DIC can indeed enable efficient similarity queries.
[Show abstract][Hide abstract] ABSTRACT: Recently, Distributed Hash Tables (DHT) explicitly designed for the use in MANETs have been proposed. Thus, many DHT-based distributed network applications from the domain of the Internet can be expected to be efficiently ported to MANETs. While the exact key lookups provided by such DHTs might be sufficient for many applications, range queries are often a desirable feature in wireless ad hoc networks (e.g. in sensor networks). However, the implementation of range queries using DHTs is a non-trivial task. In this paper we present a straight-forward implementation of Distributed Segment Trees as proposed in  on top of MADPastry  to provide DHT-based range queries for MANETs. The main goal of this work is to gain a first insight into the question whether DHT-based approaches for range queries are feasible in MANETs. First experimental results indicate that DHTs can indeed enable efficient range queries in MANETs.
[Show abstract][Hide abstract] ABSTRACT: In this paper, we attempt to approximate and index a d- dimensional (d ≥ 1) spatio-temporal trajectory with a low order continuous polynomial. There are many possible ways to choose the polynomial, including (continuous)Fourier transforms, splines, non-linear regressino, etc. Some of these possiblities have indeed been studied beofre. We hypothesize that one of the best possibilities is the polynomial that minimizes the maximum deviation from the true value, which is called the minimax polynomial. Minimax approximation is particularly meaningful for indexing because in a branch-and-bound search (i.e., for finding nearest neighbours), the smaller the maximum deviation, the more pruning opportunities there exist. However, in general, among all the polynomials of the same degree, the optimal minimax polynomial is very hard to compute. However, it has been shown thta the Chebyshev approximation is almost identical to the optimal minimax polynomial, and is easy to compute . Thus, in this paper, we explore how to use the Chebyshev polynomials as a basis for approximating and indexing d-dimenstional trajectories.The key analytic result of this paper is the Lower Bounding Lemma. that is, we show that the Euclidean distance between two d-dimensional trajectories is lower bounded by the weighted Euclidean distance between the two vectors of Chebyshev coefficients. this lemma is not trivial to show, and it ensures that indexing with Chebyshev cofficients aedmits no false negatives. To complement that analystic result, we conducted comprehensive experimental evaluation with real and generated 1-dimensional to 4-dimensional data sets. We compared the proposed schem with the Adaptive Piecewise Constant Approximation (APCA) scheme. Our preliminary results indicate that in all situations we tested, Chebyshev indexing dominates APCA in pruning power, I/O and CPU costs.
Proceedings of the ACM SIGMOD International Conference on Management of Data, Paris, France, June 13-18, 2004; 01/2004
[Show abstract][Hide abstract] ABSTRACT: Distributed topology control mechanisms for 3-dimensional settings are of considerable interest for automated network configuration in diverse applications including structural monitoring networks and underwater networks. The 3-D CBTC technique proposed by Bahramgiri et al.  has a complexity of O ( d <sup>3</sup> log d ), where d represents the average number of neighbors per node. We present two efficient alternatives. The first is a heuristic based on 2-D orthographic projections that provides excellent performance in practice, but is theoretically not guaranteed to produce a connected network. The second is a more rigorous approach based on spherical Delaunay triangulation (SDT). Both have significantly better running times that scale as O ( d log d ). Our simulation results indicate that network topologies generated based on the SDT algorithm have substantially lower average node degree and average transmission power level compared to the original network for random deployments.
Sensor, Mesh and Ad Hoc Communications and Networks, 2007. SECON '07. 4th Annual IEEE Communications Society Conference on; 07/2007
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