Voronoi diagram and convex hull based geocasting and routing in wireless networks

A broad variety of location dependent services will become feasible in the near future due to the use of the Global Positioning System (GPS), which provides location information (latitude, longitude and possibly height) and global timing to mobile users. Routing is a problem of sending a message from a source to a destination. Geocasting is a problem of sending a message to all nodes located within a region (e.g. circle or square). Recently, several localized GPS based routing and geocasting protocols for a mobile ad hoc network were reported in literature. In directional (DIR) routing and geocasting methods, node A (the source or intermediate node) transmits a message m to all neighbors located between the two tangents from A to the region that could contain the destination. It was shown that memoryless directional methods might create loops in routing process. In two other proposed methods (proven to be loop-free), geographic distance (GEDIR) or most forward progress within radius (MFR) routing, node A forwards the message to its neighbor who is closest to destination, or has greatest progress towards destination (respectively). In this paper, we propose a general algorithm (based on a unified framework for both routing and geocasting problems), in which message is forwarded to exactly those neighbors, which may be best choices for a possible position of destination (using the appropriate criterion). We then propose and discuss new V-GEDIR and CH-MFR methods and define R-DIR, modified version of existing directional methods. In V-GEDIR method, these neighbors are determined by intersecting the Voronoi diagram of neighbors with the circle (or rectangle) of possible positions of destination, while the portion of the complex hull of neighboring node is analogously used in the CH-MFR method. Routing and geocasting algorithms differ only inside the circle/rectangle. We propose memoryless and past traffic memorization variants of each scheme. The proposed methods may be also used for the destination search phase allowing the application of different routing schemes after the exact destination of position is discovered. Memoryless V-GEDIR and CH-MFR algorithms are loop-free, and have smaller flooding rate (with similar success rate) compared to directional method. Simulations involving the proposed and some known algorithms are in progress and confirm our expectations.