Topology dependent space filling curves for sensor networks and applications

Abstract

Abstract-In this paper we propose an algorithm to construct a "space filling" curve for a sensor network with holes. Mathematically, for a given multi-hole domain R, we generate a path P that is provably aperiodic (i.e., any point is covered at most a constant number of times) and dense (i.e., any point of R is arbitrarily close to P). In a discrete setting as in a sensor network, the path visits the nodes with progressive density, which can adapt to the budget of the path length. Given a higher budget, the path covers the network with higher density. With a lower budget the path becomes proportional sparser. We show how this density-adaptive space filling curve can be useful for applications such as serial data fusion, motion planning for data mules, sensor node indexing, and double ruling type in-network data storage and retrieval. We show by simulation results the superior performance of using our algorithm vs standard space filling curves and random walks.

A Unified Framework for Constrained Linearization of Sensor Networks With Arbitrary Shapes

“…Ban et al [2] propose to computes an aperiodic dense curve of 2D sensor networks with holes by first mapping all holes but one to ''slits'', and then following the line bouncing back and forth between the inner boundary of the only hole and the outer boundary. Yan and Mostofi [24] propose to linearize clustered 2D sensor networks and design path planning strategies for robotic data collection, and the simulations on a square area show that it outperforms the serial depth-first traversal scheme and the tree-based aggregation scheme in terms of message cost and detection accuracy.…”

“…Ban et al [2] exploit the computed aperiodic dense curve (i.e., the curve traverses each sensor node at most a constant number of times) of 2D sensor networks for multiple data mules coordination and double ruling based in-network data storage and retrieval. Xie et al [22] show that the shortest Hamiltonian cycle (i.e., a closed Hamiltonian path visiting each sensor) is the optimal traveling path of the wireless charging vehicle, and thus propose a novel energy renewal scheme for sensor networks.…”

“…The linearization of sensor networks computes a single path, the discrete counterpart of the SFC in a continuous domain, ''covering'' the whole network (i.e., traversing all sensors). Thanks to the capability of visiting various regions and the locality property (e.g., two close points on a 2D plane are also nearby in the SFC), the network linearization has great potential of benefiting many applications [2], such as motion planing of mobile agents for data collection (also termed as data mules) [11], [18], [24] or battery recharging [13], [22], serial/linear data fusion [14], [15], [17], spatial indexing [1], [16], just to name a few.…”

Asymptotic Consensus on the Average of a Field for Time-Varying Nonlinear Networks Under Almost Periodic Connectivity

“…Of course, coordinates in the torus need to be projected down to Euclidean coordinates when assessing relative positions of agents in the plane. This is a well defined procedure [2] usually considered for R 2 also in sensor and mobile applications ( [3]). More configuration variables could be included in θ i so as to model situations where availability of a communication channel between agents is not a function of reciprocal position alone, for instance if agents communicate through directional antennas.…”

Robot Coverage Path planning for general surfaces using quadratic differentials

“…The one most relevant was our earlier work for generating a space filling curve [27]. However, the focus in [27] was to find a curve with progressive density -that is, we want a path such that the distance from any point to the path to be shrinking progressively when the path gets longer. The same as in a followup work [28].…”