In this work, we present a new approach for competitive geometric routing in wireless ad hoc networks. In general, it is well-known that any online routing strategy performs very poor in the worst case. The main difficulty are uncovered regions within the wireless ad hoc network, which we denote as radio holes. Complex shapes of radio holes, for example zig-zag-shapes, make local geometric routing even more difficult, i.e., forwarded messages in direction to the destination might get stuck in a dead end or are routed along very long detours, when there is no knowledge about the ad hoc network. To obtain knowledge about the position and shape of radio holes, we make use of a hybrid network approach. This approach assumes that we can not just make use of the ad hoc network but also of some cellular infrastructure, which is used to gather knowledge about the underlying ad hoc network. Communication via the cellular infrastructure incurs costs as cell phone providers are involved. Therefore, we use the cellular infrastructure only to compute routing paths in the ad hoc network. The actual data transmission takes place in the ad hoc network. In order to find good routing paths we aim at computing an abstraction of the ad hoc network in which radio holes are abstracted by bounding boxes. The advantage of bounding boxes as hole abstraction is that we only have to consider a constant number of nodes per hole. We prove that bounding boxes are a suitable hole abstraction that allows us to find @math -competitive paths in the ad hoc network in case of non-intersecting bounding boxes. In case of intersecting bounding boxes, we show via simulations that our routing strategy significantly outperforms the so far best online routing strategies for wireless ad hoc networks. Finally, we also present a routing strategy that is @math -competitive in case of pairwise intersecting bounding boxes.
@cite_2: Routing is a challenging problem for wireless ad hoc networks, especially when the nodes are mobile and spread so widely that in most cases multiple hops are needed to route a message from one node to another. In fact, it is known that any online routing protocol has a poor performance in the worst case, in a sense that there is a distribution of nodes resulting in bad routing paths for that protocol, even if the nodes know their geographic positions and the geographic position of the destination of a message is known. The reason for that is that radio holes in the ad hoc network may require messages to take long detours in order to get to a destination, which are hard to find in an online fashion.
The approach we extend in this work makes use of global information as well @cite_2 . The global information is gathered via a Hybrid Communication Network. In a Hybrid Communication Network, nodes can communicate with other nodes in their ad hoc range for free. In addition, they can use long-range links to communicate with any other node of the network. These long-range links, the Cellular Infrastructure, are costly. The solution they propose is to compute an Overlay Network in which holes are represented by their convex hulls. It is assumed that the convex hulls of the holes do not intersect. The storage requirements for some nodes are asymptotically in the size of the sum of all holes. In this work, we aim to reduce the storage requirements for these nodes and investigate also the challenging question of @math -competitive routing through intersections of hole abstractions.