  This paper considers a dynamic coverage problem for sensor networks that are
sufficiently dense but not localized. Only a small fraction of sensors may be
in an awake state at any given time. The goal is to find a decentralized
protocol for establishing dynamic, sweeping barriers of awake-state sensors.
Following Baryshnikov-Coffman-Kwak, we use network cyclic cellular automata to
generate waves. This paper gives a rigorous analysis of network-based cyclic
cellular automata in the context of a system of narrow hallways and shows that
waves of awake-state nodes turn corners and automatically solve
pusuit/evasion-type problems without centralized coordination.
  As a corollary of this work, we unearth some interesting topological
interpretations of features previously observed in cyclic cellular automata
(CCA). By considering CCA over networks and completing to simplicial complexes,
we induce dynamics on the higher-dimensional complex. In this setting, waves
are seen to be generated by topological defects with a nontrivial degree (or
winding number). The simplicial complex has the topological type of the
underlying map of the workspace (a subset of the plane), and the resulting
waves can be classified cohomologically. This allows one to "program" pulses in
the sensor network according to cohomology class. We give a realization theorem
for such pulse waves.
