Optimal polling in communication networks

Polling is the process in which an issuing node of a communication network (polling station) broadcasts a query to every other node in the network and must receive a unique response from each of them. Polling can be thought as a combination of broadcasting and gathering and finds wide applications in the control of distributed systems. In this paper we consider the problem of polling in minimum time. We give a general lower bound on the minimum number of time units to accomplish polling in any network and we present optimal polling algorithms for several classes of graphs, including hypercubes and recursively decomposable Cayley graphs.