Towards Desynchronization of Multi-hop Topologies

In this paper we study desynchronization, a closely related primitive to graph coloring. A valid graph coloring is an assignment of colors to nodes such that no node's color is the same as a neighborpsilas. A desynchronized configuration is an assignment of real values in S1 to nodes such that each nodepsilas value is exactly at the midpoint of two of its closest neighborspsila values. Recent work has shown that a simple, self-organizing algorithm, DESYNC,can solve desynchronization in single-hop networks, with applications to collision-free wireless broadcast and duty-cycling. Here we generalize this work by defining and analyzing desynchronization for multi-hop networks and experimentally analyzing the DESYNC algorithm's behavior for multi-hop networks. We describe desynchronized configurations for several classes of graphs (lines, rings, two-colorable, and Hamiltonian cycles) and discuss the relationship with other variants of graph coloring. We extend the DESYNC algorithm and DESYNC-based resource allocation to multi-hop networks and study the performance and efficiency of resource allocation in simulation. While many applications for graph coloring require synchronization and an agreement on a schedule to be effective, we show that the self-organizing algorithm, DESYNC, does not require either of these to achieve desynchronization and to define a resource-allocation schedule. Although applications to wireless sensor networks pose some unique problems, the results suggest that DESYNC has significant potential as a lightweight method for providing non-overlapping variable-sized slots in ad-hoc multi-hop settings.