Gradient-Based Distance Estimation for Spatial Computers

Abstract

Today's wireless networks are connecting more and more devices around us, leading to the birth of a new distributed computing platform, in the form of a spatial computer. The main difference with traditional computing models is that space and time become intertwined with computation, especially when scaling up the system. Computations performed by each element are now related to its spatial position. This property is the key ingredient when assuring the availability for various distributed networking services and applications. Computations become linked to the concept of space. Estimating distances between components (especially in dynamic networks characterized by the node mobility) thus becomes one of the most important building blocks for spatial computing. The majority of the algorithms that come from the MANET community presume knowledge about node position via systems such as GPS, or employ a one-time manual network topology configuration. While for some application scenarios this approach is feasible, for a lot of cases it suffers from frequent unavailability (e.g. indoors) and high costs in terms of energy consumption. Therefore, intense demand exists for a new kind of distance estimation algorithm using only simple local interactions, without knowledge of global information. The main contribution of the article is the introduction of a novel distributed algorithm, called gradient-based distance estimation (GDE), for the estimation of distances in networks characterized by mobility, specifically targeting the context of spatial computing. GDE is based on a gossiping mechanism to estimate distances between nodes with only local interactions. It significantly improves current state of the art by employing statistical analysis and making better use of the information available at each node.We analyze the parameters that should be considered by real applications, and present mathematical models to compensate their influence for distance estimation. Three spatial computing applications using GDE are presented: geographical cluster center detection, topological overlay shape construction and geographic routing. The simulation-based evaluation shows that GDE succeeds in estimating the distance between nodes in both static and mobile scenarios with considerably high accuracy for various simulations setups, such as varying node density, node speed or spatial node distribution.