Processing Convex Hull Queries in MANETs

Location-based service (LBS) is a typical application for mobile ad hoc networks (MANETs). In an LBS, it is effective for nodes to acquire data using convex hull queries, which retrieve the information necessary for calculating the convex hull of all nodes composing a given network. In a naive approach, the query-issuing node can determine the convex hull of the network by flooding a query throughout the entire network and receiving location information on all the nodes, but this involves excessive traffic. In addition, since the network topology changes dynamically, due to the movement of nodes, the set of vertices of the convex hull changes. Therefore, the query-issuing node must determine the convex hull in a short period of time. In this paper, we propose convex hull query processing methods for reducing traffic and response time while maintaining high accuracy of the query result in MANETs. In these methods, nodes reply with information on nodes which are convex hull vertices. In the Local Convex Hull (LCH) method, nodes reply with information on nodes which are vertices of the local convex hull, which is the convex hull composed of nodes whose information has already been received. In the Local Wrapping (LW) method, the query is transmitted only to nodes on the outer boundary. Experimental results show that our proposed methods reduce traffic and achieve short response time and high accuracy of the query result, in comparison with a naive method.