Bounded-hop energy-efficient liveness of 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. In the first phase, nodes construct a temporary underlying topology and disseminate their current location and mobility plans. This is followed by a second phase, in which nodes construct the desired topology under two modes: static and dynamic. The static mode provides a fixed topology which does not change in spite of node movements; the dynamic mode allows the topology to change; however, the hop-diameter remains the same. We provide an O(λ,λ2)-bicriteria approximation (in terms of total energy consumption and network lifetime, respectively) algorithm in the static mode: for an input parameter λ, we construct a static h-bounded hop communication graph, where h=nλ + logλ. In the dynamic mode, given a parameter h, we construct an optimal (in terms of network lifetime) h-bounded hop communication graph when every node moves with constant speed in a single direction along a straight line during each time interval. Our results are validated through extensive simulations.