Time and Space Efficient Graph Exploration by a Mobile Agent Using Whiteboard

摘要

We consider the exploration problem with a single agent in undirected graphs. Starting from an arbitrary node, the agent has to explore all the nodes and edges in the graph and return to the starting node. Our goal is to minimize both the number of agent moves and the memory space of the agent, which dominate the amount of communication during the exploration. In our setting, the agent is allowed to use the local memory called the whiteboard on each node (the whiteboard model), while most of existing exploration algorithms do not use the whiteboard (the no-whiteboard model). In the no-whiteboard model, the agent must memorize in its memory all information needed to explore the graph, and thus designing an exploration algorithm of small agent memory is difficult. In this paper, by allowing the agent to use whiteboards, we present four exploration algorithms such that both the number of agent moves and the agent memory space are small.