Fast Graph Exploration by a Mobile Robot

Given an undirected, anonymous, port-labeled graph of n nodes, m edges, and degree Delta, we require a mobile robot to visit all the nodes in the graph. We give two algorithms to solve this problem in O(m) time. Algorithm Robot-Memory uses O(n log Delta) bits at the robot, and 1 bit at each node. Algorithm Node-Memory uses O(log Delta) bits at each node. The algorithms Robot-Memory and Node-Memory trade-off the memory requirements at the robot and at the nodes. The algorithms are capable of perpetual exploration or patrolling, and are variants of depth-first search (DFS). The algorithms fill in existing gaps in the trade-offs between robot memory, memory at each node, and exploration time, in the body of literature on the graph exploration problem.