We consider the fundamental task of network exploration. A network is modeled as a simple connected undirected n-node graph with unlabeled nodes, and all ports at any node of degree d are arbitrarily numbered 0,.....,d-1. Each of two identical mobile agents, initially situated at distinct nodes, has to visit all nodes and stop. Agents execute the same deterministic algorithm and move in synchronous rounds: in each round, an agent can either remain at the same node or move to an adjacent node. Exploration must be collision-free: in every round at most one agent can be at any node. We assume that agents have vision of radius 2: an awake agent situated at a node v can see the subgraph induced by all nodes at a distance at most 2 from v, sees all port numbers in this subgraph, and the agents located at these nodes. Agents do not know the entire graph but they know an upper bound n on its size. The time of an exploration is the number of rounds since the wakeup of the later agent to the termination by both agents. We show a collision-free exploration algorithm working in time polynomial in n, for arbitrary graphs of size larger than 2. Moreover, we show that if agents have only vision of radius 1, then collision-free exploration is impossible, e.g., in any tree of diameter 2.

翻译：我们考虑网络探索的基本任务。网络建模为一个简单连通无向的n节点图，节点无标签，且任意度为d的节点的所有端口被任意编号为0,...,d-1。两个相同的移动代理初始位于不同节点，每个代理需访问所有节点并停止。代理执行相同的确定性算法，并在同步轮次中移动：每轮中，代理可停留在同一节点或移动到相邻节点。探索必须无碰撞：每轮中任一节点上最多只能有一个代理。我们假设代理具有半径为2的视野：位于节点v的清醒代理可看到距离v不超过2的所有节点所诱导的子图，看到该子图中的所有端口编号，以及位于这些节点上的代理。代理不知道整个图，但知道其大小的上界n。探索时间定义为从较晚唤醒的代理开始到两个代理均终止所经过的轮数。我们给出一个对任意大于2规模的图均在n的多项式时间内工作的无碰撞探索算法。此外，我们证明若代理仅具有半径为1的视野，则无碰撞探索不可能实现，例如在任何直径为2的树中。