Topology Preserving Maps—Extracting Layout Maps of Wireless Sensor Networks From Virtual Coordinates

A method for obtaining topology-preserving maps (TPMs) from virtual coordinates (VCs) of wireless sensor networks is presented. In a virtual coordinate system (VCS), a node is identified by a vector containing its distances, in hops, to a small subset of nodes called anchors. Layout information such as physical voids, shape, and even relative physical positions of sensor nodes with respect to x- y directions are absent in a VCS description. The proposed technique uses Singular Value Decomposition to isolate dominant radial information and to extract topological information from the VCS for networks deployed on 2-D/3-D surfaces and in 3-D volumes. The transformation required for TPM extraction can be generated using the coordinates of a subset of nodes, resulting in sensor-network-friendly implementation alternatives. TPMs of networks representing a variety of topologies are extracted. Topology preservation error ( ETP), a metric that accounts for both the number and degree of node flips, is defined and used to evaluate 2-D TPMs. The techniques extract TPMs with ( ETP) less than 2%. Topology coordinates provide an economical alternative to physical coordinates for many sensor networking algorithms.