Abstract
A random method for exploring a continuous unknown planar domain with almost no sensors is described. The expected cover time is shown to be proportional to the electrical resistance of the domain, thus extending an existing result for graphs [11]. An upper bound on the variance is also shown, and some open questions are suggested for further research.
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Wagner, I.A., Lindenbaum, M., Bruckstein, A.M. (1998). Robotic Exploration, Brownian Motion and Electrical Resistance. In: Luby, M., Rolim, J.D.P., Serna, M. (eds) Randomization and Approximation Techniques in Computer Science. RANDOM 1998. Lecture Notes in Computer Science, vol 1518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49543-6_10
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