Low Memory Distributed Protocols for 2-Coloring

In this paper we present new distributed protocols to color even rings and general bipartite graphs. Our motivation is to provide algorithmic explanation for human subject experiments that show human subjects can achieve distributed coordination in the form of 2-coloring over networks with a simple communication protocol. All our protocols use low (often constant) memory and reach a solution in feasible (polynomial rounds) and sometimes optimal time. All the protocols also have short message length and use a broadcast communication strategy. Our contributions include two simple protocols

RingElect

and

GraphCoalescing

for rings and general bipartite graphs, which can be viewed as candidates for natural human strategies. We present two other protocols

RingElect

and

GraphElect

which are optimal or nearly optimal in terms of the number of rounds (proportional to the diameter of the graph) but require somewhat more complex strategies. The question of finding simple protocols in the style of

RingElect

and

GraphCoalescing

that run in time proportional to diameter is open.