Assessing standard and inverted skip graphs using multi-dimensional range queries and mobile nodes

The skip graph, an application-layer data structure for routing and indexing, may he used in a sensor network to facilitate queries of the distributed k-dimensional data collected by the nodes, such as their geographic positions. Nodes in a standard skip graph sort keys in layered groups, where group membership is determined by random membership vectors. We propose a skip graph extension that inverts the key and membership vector roles, wherein group membership is based on deterministic z-ordering of k-dimensional data and sorting within groups is based on random keys. This extension retains the structure of a standard skip graph, and can be modified for use in 3-D environments such as unmanned aerial vehicle swarms. Our results indicate this extension reduces the number of nodes contacted relative to the query precision, the volume of the multidimensional space, and the skip graph's height. We discuss our extension's performance relative to metrics at the application and network layers for static and mobile 2-D networks.