Brief Announcement: Fault Tolerant Coloring of the Asynchronous Cycle

We present a wait-free algorithm for proper coloring the n >= 3 nodes of the asynchronous cycle C-n, where each crash-prone node starts with its (unique) identifier as input. The algorithm is independent of.. and uses up to five colors, and each node terminates upon completing at most O( log*n) write-read-compute steps. Coloring the asynchronous 3-nodes cycle C-3 coincides with renaming a 3-processes system using an immediate snapshot object, which cannot be solved with less than five names in a wait-free manner. Moreover, in the synchronous and failure-free LOCAL model, graph coloring has a known round complexity of Theta T( log*n). Thus, no algorithm can color all asynchronous cycles using fewer colors, or with an asymptotically smaller step complexity.