The Power of Team Exploration: Two Robots Can Learn Unlabeled Directed Graphs

We show that two cooperating robots can learn exactly any strongly-connected directed graph with n indistinguishable nodes in expected time polynomial in n. We introduce a new type of homingsequence 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 sequence simultaneously by actively wandering through the graph. Unlike most previous learning results using homing sequences, our algorithm does not require a teacher to provide counterexamples. Furthermore, the algorithmcan use e ciently any additional informationavailable that distinguishes nodes. We also present an algorithm in which the robots learn by taking random walks. The rate at which a random walk on a graph converges to the stationary distribution is characterized 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 e cient t...

• Type: Conference
• Year: 1994
• Where: FOCS
• Authors: Michael A. Bender, Donna K. Slonim
• Keywords: Algorithm, Expected Time Polynomial, FOCS 1994, Robots, Theoretical Computer Science