Design of Combined Coverage Area Reporting and Geo-casting of Queries for Wireless Sensor Networks

In order to efficiently deal with queries or other location dependent information, it is key that the wireless sensor network informs gateways what geographical area is serviced by which gateway. The gateways are then able to e.g. efficiently route queries which are only valid in particular regions of the deployment. The proposed algorithms combine coverage area reporting and geographical routing of queries which are injected by gateways.\u

Combined Coverage Area Reporting and Geographical Routing in Wireless Sensor-Actuator Networks for Cooperating with Unmanned Aerial Vehicles

In wireless sensor network (WSN) applications with multiple gateways, it is key to route location dependent subscriptions efficiently at two levels in the system. At the gateway level, data sinks must not waste the energy of the WSN by injecting subscriptions that are not relevant for the nodes in their coverage area and at WSN level, energy-efficient delivery of subscriptions to target areas is required. In this paper, we propose a mechanism in which (1) the WSN provides an accurate and up-to-date coverage area description to gateways and (2) the wireless sensor network re-uses the collected coverage area information to enable efficient geographical routing of location dependent subscriptions and other messages. The latter has a focus on routing of messages injected from sink nodes to nodes in the region of interest. Our proposed mechanisms are evaluated in simulation

On Mobility Management in Multi-Sink Sensor Networks for Geocasting of Queries

In order to efficiently deal with location dependent messages in multi-sink wireless sensor networks (WSNs), it is key that the network informs sinks what geographical area is covered by which sink. The sinks are then able to efficiently route messages which are only valid in particular regions of the deployment. In our previous work (see the 5th and 6th cited documents), we proposed a combined coverage area reporting and geographical routing protocol for location dependent messages, for example, queries that are injected by sinks. In this paper, we study the case where we have static sinks and mobile sensor nodes in the network. To provide up-to-date coverage areas to sinks, we focus on handling node mobility in the network. We discuss what is a better method for updating the routing structure (i.e., routing trees and coverage areas) to handle mobility efficiently: periodic global updates initiated from sinks or local updates triggered by mobile sensors. Simulation results show that local updating perform very well in terms of query delivery ratio. Local updating has a better scalability to increasing network size. It is also more energy efficient than ourpreviously proposed approach, where global updating in networks have medium mobility rate and speed

Output-Sensitive Tools for Range Searching in Higher Dimensions

Let $P$ be a set of $n$ points in ${\mathbb R}^{d}$. A point $p \in P$ is $k$\emph{-shallow} if it lies in a halfspace which contains at most $k$ points of $P$ (including $p$). We show that if all points of $P$ are $k$-shallow, then $P$ can be partitioned into $\Theta(n/k)$ subsets, so that any hyperplane crosses at most $O((n/k)^{1-1/(d-1)} \log^{2/(d-1)}(n/k))$ subsets. Given such a partition, we can apply the standard construction of a spanning tree with small crossing number within each subset, to obtain a spanning tree for the point set $P$, with crossing number $O(n^{1-1/(d-1)}k^{1/d(d-1)} \log^{2/(d-1)}(n/k))$. This allows us to extend the construction of Har-Peled and Sharir \cite{hs11} to three and higher dimensions, to obtain, for any set of $n$ points in ${\mathbb R}^{d}$ (without the shallowness assumption), a spanning tree $T$ with {\em small relative crossing number}. That is, any hyperplane which contains $w \leq n/2$ points of $P$ on one side, crosses $O(n^{1-1/(d-1)}w^{1/d(d-1)} \log^{2/(d-1)}(n/w))$ edges of $T$. Using a similar mechanism, we also obtain a data structure for halfspace range counting, which uses $O(n \log \log n)$ space (and somewhat higher preprocessing cost), and answers a query in time $O(n^{1-1/(d-1)}k^{1/d(d-1)} (\log (n/k))^{O(1)})$, where $k$ is the output size

Convex Hulls under Uncertainty

We study the convex-hull problem in a probabilistic setting, motivated by the need to handle data uncertainty inherent in many applications, including sensor databases, location-based services and computer vision. In our framework, the uncertainty of each input site is described by a probability distribution over a finite number of possible locations including a \emph{null} location to account for non-existence of the point. Our results include both exact and approximation algorithms for computing the probability of a query point lying inside the convex hull of the input, time-space tradeoffs for the membership queries, a connection between Tukey depth and membership queries, as well as a new notion of \some-hull that may be a useful representation of uncertain hulls

Incremental and Decremental Maintenance of Planar Width

We present an algorithm for maintaining the width of a planar point set dynamically, as points are inserted or deleted. Our algorithm takes time O(kn^epsilon) per update, where k is the amount of change the update causes in the convex hull, n is the number of points in the set, and epsilon is any arbitrarily small constant. For incremental or decremental update sequences, the amortized time per update is O(n^epsilon).Comment: 7 pages; 2 figures. A preliminary version of this paper was presented at the 10th ACM/SIAM Symp. Discrete Algorithms (SODA '99); this is the journal version, and will appear in J. Algorithm