  We introduce a simple tool called the wavelet (or, r-wavelet) scheme.
Wavelets deals with coordination among processes which are at most r hops away
of each other. We present a selfstabilizing solution for this scheme. Our
solution requires no underlying structure and works in arbritrary anonymous
networks, i.e., no process identifier is required. Moreover, our solution works
under any (even unfair) daemon. Next, we use the wavelet scheme to design
self-stabilizing layer clocks. We show that they provide an efficient device in
the design of local coordination problems at distance r, i.e., r-barrier
synchronization and r-local resource allocation (LRA) such as r-local mutual
exclusion (LME), r-group mutual exclusion (GME), and r-Reader/Writers. Some
solutions to the r-LRA problem (e.g., r-LME) also provide transformers to
transform algorithms written assuming any r-central daemon into algorithms
working with any distributed daemon.
