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：本文研究多智能体在线图探索问题，其中k个智能体团队需从同一节点出发并返回，探索给定图结构。图初始不可知，每当智能体访问某节点时，其邻域及相邻边即被揭示。智能体共享已探索部分的全局视图。需最小化探索成本，成本可描述为整个探索所需的时间（时间模型），或任一智能体遍历的最长路径长度（能量模型）。我们针对2至4个智能体的环图与蝌蚪图展开探索研究，在能量模型下给出竞争比最优结果（环图中2个智能体与蝌蚪图中3个智能体可达1-竞争性），在时间模型下对蝌蚪图（4个智能体可达1.5-竞争性）取得最优结果。同时证明了蝌蚪图探索过程中，时间模型下3个智能体的竞争比上界为2，2个智能体的竞争比上界为2.5。