Information-Theoretic Lower Bounds on the Routing Overhead in Mobile Ad-hoc Networks

In coding theory, a channel coding algorithm is good if it achieves the Shannon capacity [1]. Similarly, we seek to derive a universal curve against which we can measure how good (or bad) a variable topology routing protocol (e.g. for ad-hoc networks) performs, in comparison with a theoretical minimum routing overhead, which is the amount of information needed to describe the changes in a dynamic network topology. As a first step in this direction, we consider the following abstract model for the class of hierarchical routing protocols. A network of identical but distinguishable nodes lies within a bounded region of space. Each node moves independently. The whole region is divided into M non-overlapping sub-regions. Each sub-region has its own identifier. There are two levels of hierarchy for nodes. All the nodes of a subregion form a cluster and randomly select a cluster head from the nodes within the same sub-region. It is possible that a sub-region becomes empty and thus will not have a cluster or a cluster head. Each sub-region has a fixed number of neighbors K. A cluster-head maintains two types of topology information: (i) Local cluster topology information, denoted by IL , which describes a snapshot of the topology within the boundaries of its sub-region, and (ii) Global topology information, denoted by IG, which describes the aggregated topology of the whole network. A cluster-head needs to maintain only a simplified aggregated view of the global topology. This can be described simply as a table that lists, for each sub-region, the member nodes and the cluster-head. Node movements within the same region do not change the cluster membership, and hence do not affect IG. For simplicity, we also assume that local node movements do not affect IL i.e. that the local topology is uniquely defined by the identity of the nodes within the subregion and the identity of the cluster-head. Theorem 1 IG = log min(N,M) ∑