Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, September 19, 2017, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Emo Welzl

Lower Bounds for Searching Robots, some Faulty

We consider the following generalization of the classical "cow path problem". Suppose we are sending out k robots from 0 to search the real line at constant speed (with turns) to find a target at an unknown location; f of the robots are faulty (of so-called crash type), meaning that they fail to report the target although visiting its location. The goal is to find the target in time at most λ|d|, if the target is located at d, |d|≥1, for λ as small as possible. We show that it cannot be achieved for λ < 2*(1+ρ)^{1+ρ}/ρ^ρ + 1, ρ := 2*(f+1)/k − 1, which is tight due to earlier work. This also gives some better than previously known lower bounds for so-called Byzantine-type faulty robots (that may, deceitfully, actually wrongly report a target). (Joint work with Andrey Kupavskii.)

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