We present the design and theoretical analysis of a novel algorithm termed least recently visited (LRV). LRV efficiently and simultaneously solves the problems of coverage, exploration, and sensor network deployment. The basic premise behind the algorithm is that a robot carries network nodes as a payload, and in the process of moving around, emplaces the nodes into the environment based on certain local criteria. In turn, the nodes emit navigation directions for the robot as it goes by. Nodes recommend directions least recently visited by the robot, hence, the name LRV. We formally establish the following two properties: 1) LRV is complete on graphs and 2) LRV is optimal on trees. We present experimental conjectures for LRV on regular square and cube lattice graphs and compare its performance empirically to other graph exploration algorithms. We study the effects of the order of the exploration and show on a square lattice that with an appropriately chosen order, LRV performs optimally. Finally, we discuss the implementation of LRV in simulation and in real hardware.
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