Hybrid Position-Based Routing Algorithms for 3D Mobile Ad Hoc Networks Song Liu, Thomas Fevens, and Alaa Eddien Abdallah Department of Computer Science and Software Engineering Concordia University, Montr´ eal, QC, Canada, H3G 1M8 Email: pinestay@msn.com,{fevens,ae abdal}@cse.concordia.ca Abstract Numerous routing algorithms have been proposed for routing efficiently in mobile ad hoc networks (MANETs) embedded in two dimensional (2D) spaces. But, in prac- tice, such networks are frequently arranged in three dimen- sional (3D) spaces where the assumptions made in two di- mensions, such as the ability to extract a planar subgraph, break down. Recently, a new category of 3D position-based routing algorithms based on projecting the 3D MANET to a projection plane has been proposed. In particular, the Adaptive Least-Squares Projective (ALSP) Face routing al- gorithm (Kao et al., 2007) achieves nearly guaranteed de- livery but usually discovers excessively long routes to the destination. Referencing the idea of hybrid Greedy-Face- Greedy (GFG) routing in 2D MANETs, we propose a lo- cal hybrid algorithm combining Greedy routing with ALSP Face routing on projection planes. We show experimen- tally that this hybrid ALSP GFG routing algorithm on static 3D ad hoc networks can achieve nearly guaranteed deliv- ery while discovering routes significantly closer in length to shortest paths. The mobility of nodes is handled by intro- ducing the concepts of active sole nodes and a limited form of flooding called residual path finding to the ALSP GFG routing algorithm. To further analyze the performance of this mobility-aware hybrid algorithm, we define a mobil- ity model for 3D MANETs. Using this mobility model, we demonstrate that the mobility-adapted hybrid routing algo- rithm can maintain high delivery rates with decreases in the average lengths of the paths discovered compared to short- est paths, without generating a large amount of flooding traffic. 1. Introduction A wireless ad hoc network is a collection of wireless hosts that can communicate without a fixed infrastructure. Each host in the network can communicate with all other hosts within its transmission range [4, 5], which we will assume for this paper to be a fixed range R for all hosts. If two hosts are not able to communicate directly then a multi- hop routing protocol is needed for the hosts to send packets to each other. Since the wireless hosts that we are model- ing commonly have only have a limited power supply (such as a battery) and a limited amount of memory, particularly for ad hoc sensor networks, local algorithms are typically preferred. A local algorithm uses only the information on neighboring nodes up to a fixed number of hops away. We are specifically interested in position-based routing proto- cols where a node forwards packets using the location (co- ordinates in the plane or space) of itself, its neighbors (up to a fixed number of hops away), and the destination [13]. Many routing algorithms have been proposed and stud- ied extensively in the context of two dimensional (2D) spaces during the past few years [13, 22]. But in the real world, e.g., in modern high-rise buildings, in rough terrain, or in outer space, hosts are naturally positioned in a three dimensional (3D) space where some assumptions made in 2D, such as the ability to extract planar subgraphs, break down. For example, in underwater acoustic sensor net- works, sensors may be deployed to monitor and report on phenomena within an underwater volume [24]. Thus for practical applications, routing algorithms for 3D ad hoc net- works should also be considered. Ideally, such a local rout- ing algorithm should guarantee delivery without resorting to flooding, but as shown by Durocher et al. [10], it is not possible to have a local routing algorithm with guaranteed delivery if the nodes of the 3D ad hoc network are contained in a slab of thickness greater than 1/ √ 2. Therefore, one ob- jective of this paper is to present local position-based rout- ing algorithms on unrestricted static 3D ad hoc networks that have nearly guaranteed delivery with discovered routes being close to the shortest paths on average. As an added complication, the hosts in a 3D ad hoc net- work may be mobile, with wireless mobile hosts possibly moving to new positions during routing. In a mobile ad hoc