Improved Distributed Exploration of Anonymous Networks

The problem of constructing a labeled map of an anonymous and asynchronous network is addressed. We present an algorithm that explores and maps the network by using k identical agents that have no prior knowledge of the network topology. An algorithm of Das, Flocchini, Nayak and Santoro for mapping of the network requires that n and k are co-prime. Our improved algorithm, presented here, requires at most O(m·logk) edge traversals, while theirs uses O(m·k) edge traversals (m is the number of edges in the network). The size of the whiteboard memory needed in our algorithm is the same as that used in DFNS algorithm O(logn). We employ techniques utilized in solutions to the Leader Election task, and introduce a modification to resolve issues of electing first “local leaders” among adjacent candidates, which otherwise may deadlock the process.