Abstract

We show that two cooperating robots can learn ex-actly any strongly-connected directed graph with n in-distinguishable nodes in expected tame polynomial in n. We introduce a new type of homing sequence for two robots which helps the robots recognize certain previously-seen nodes. We then present an algorithm in which the robots learn the graph and the homing se-quence simultaneously by wandering actively through the graph. Unlike most previous learning results us-ang homing sequences, our algorithm does not require a teacher to provide counterexamples. Furthermore, the algorithm can use efficiently any additional infor-mation available that distinguishes nodes. We also present an algorithm in which the robots learn by tak-ing random walks. The rate at which a random walk converges to the stationary distribution is character-ized by the conductance of the graph. Our random-walk algorithm learns in expected time polynomial in n and in the inverse of the conductance and is more eficient than the homing-sequence algorithm for high-conductance graphs. 1

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