Homotopy theory and distributed computing

Algebraic topology has proved to be a very useful tool in addressing the computability of rendezvous problems in distributed computing. To date the tools used include the fundamental group and ordinary homology. This paper introduces more sophisticated techniques from homotopy theory involving the Hilton-Milnor Theorem in order to analyze whether rendezvous problems are solvable. A criterion is proved that ensures a solution given certain hypotheses. Families of examples are given when the hypotheses are satisfied and when they are not satisfied; these include new cases when homology alone suffices to ensure a solution and cases when homology needs to be supplemented by additional properties to obtain a solution.