Faster Treasure Hunt and Better Strongly Universal Exploration Sequences

We study the explicit deterministic treasure hunt problem in an n-vertex network. This problem was firstly introduced by Ta-Shma, and Zwick in [9] [SODA'07]. It is the variant of the well known rendezvous problem in which one of the robot (the treasure) is always stationary. We obtain an O(nc(1+ 1/λ))- time solution for this problem, which significantly improves the currently best known result of running time O(n2c) in [9], where c is a fixed constant from the construction of an universal exploration sequence in [8,9], λ is a constant integer and λ ≫ 1. The treasure hunt problem motivates the study of strongly universal exploration sequences. We give a better explicit construction of strongly universal exploration sequences than the one in [9].

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