We seek exploration algorithms for which this worst-case ratio is the smallest. We consider scenarios where the robot has no knowledge of the graph and when it has an unoriented map (isomorphic copy) of it.
A problem related to graph exploration is rendezvous in graphs. Two mobile agents having distinct identifiers and located in nodes of an unknown anonymous connected graph, have to meet at some node of the graph. We seek fast deterministic algorithms for this rendezvous problem, under two scenarios:
- simultaneous startup, when both agents start executing the algorithm at the same time, and
- arbitrary startup, when starting times of the agents are arbitrarily decided by the adversary.