Deterministic Collision-Free Exploration of Unknown Anonymous Graphs
CoRR(2024)
摘要
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.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要