We study the problem of multi-agent online graph exploration, in which a team of k agents has to explore a given graph, starting and ending on the same node. The graph is initially unknown. Whenever a node is visited by an agent, its neighborhood and adjacent edges are revealed. The agents share a global view of the explored parts of the graph. The cost of the exploration has to be minimized, where cost either describes the time needed for the entire exploration (time model), or the length of the longest path traversed by any agent (energy model). We investigate graph exploration on cycles and tadpole graphs for 2-4 agents, providing optimal results on the competitive ratio in the energy model (1-competitive with two agents on cycles and three agents on tadpole graphs), and for tadpole graphs in the time model (1.5-competitive with four agents). We also show competitive upper bounds of 2 for the exploration of tadpole graphs with three agents, and 2.5 for the exploration of tadpole graphs with two agents in the time model.

翻译：我们研究多智能体在线图探索问题，其中由k个智能体组成的团队需探索给定图，起点与终点均为同一节点。初始状态下图结构未知，每当智能体访问某节点时，其邻域及相邻边会被揭示。智能体共享已探索部分的全局视图。优化目标是最小化探索成本，成本模型分为两类：时间模型（描述整个探索所需时间）和能量模型（描述任意智能体最长路径长度）。针对2-4个智能体，我们研究了环图与蝌蚪图上的图探索问题，在能量模型（环图双智能体与蝌蚪图三智能体实现1-竞争比）及时间模型（蝌蚪图四智能体实现1.5-竞争比）中给出了最优竞争比结果。此外，我们证明了时间模型下三智能体探索蝌蚪图的竞争比上界为2，双智能体探索蝌蚪图的竞争比上界为2.5。