Bounded-hop strong connectivity for flocking swarms

In this paper we consider a set of n mobile wireless nodes, which have no information about each other. The only information a single node holds is its current location and future mobility plan. We develop a two-phase distributed self-stabilizing scheme for producing a bounded hop-diameter communication graph. The first phase is dedicated to the construction of an underlying topology for the dissemination of data needed for the second phase. In the second phase the required topology is constructed by means of an asymmetric power assignment under two modes - static and dynamic. The former aims to provide a steady topology for some time interval, while the latter uses the constant node locations changes to produce a constantly changing topology, which succeeds to preserve the required property of the bounded hop-diameter. For the static mode we provide an O(λ,λ²)-bicriteria approximation algorithm so that given a parameter 1 ≤ λ ≤ n-1, we construct a power assignment which induces a static h-bounded hop communication graph, h=n/λ+logλ, with a cost of at most λ times the optimum and network lifetime of at least 1/λ² times the optimum. For the dynamic mode, given a parameter 1 ≤ h ≤ n-1 we construct an optimal power assignment (in terms of network lifetime) which induces a dynamic h-bounded hop communication graph.