Connectivity-Based Space Filling Curve Construction Algorithms in High Genus 3D Surface WSNs

Many applications in wireless sensor networks (WSNs) require that sensor observations in a given monitoring area are aggregated in a serial fashion. This demands a routing path to be constructed traversing all sensors in that area, which is also needed to linearize the network. In this article, we present SURF, a Space filling cURve construction scheme for high genus three-dimensional (3D) surFace WSNs, yielding a traversal path provably aperiodic (that is, any node is covered at most a constant number of times). SURF first utilizes the hop-count distance function to construct the iso-contour in discrete settings, and then it uses the concept of the Reeb graph and the maximum cut set to divide the network into different regions. Finally, it conducts a novel serial traversal scheme, enabling the traversal within and between regions. To the best of our knowledge, SURF is the first high genus 3D surface WSN targeted and pure connectivity-based solution for linearizing the networks. It is fully distributed and highly scalable, requiring a nearly constant storage and communication cost per node in the network. To incorporate adaptive density of the constructed space filling curve, we also design a second algorithm, called SURF+, which makes use of parameterized spiral-like curves to cover the 3D surface and thus can yield a multiresolution SFC adapting to different requirements on travel budget or fusion delay. The application combining both algorithms for in-network data storage and retrieval in high genus 3D surface WSNs is also presented. Extensive simulations on several representative networks demonstrate that both algorithms work well on high genus 3D surface WSNs.