Faster Treasure Hunt and Better Strongly Universal Exploration Sequences

In this paper, we investigate the explicit deterministic treasure hunt problem in a n-vertex network. This problem was firstly introduced by Ta-Shma and Zwick in [10] [SODA’07]. Note also it is a variant of the well known rendezvous problem in which one of the robot (the treasure) is always stationary. In this paper, we propose an O(n 1 λ )-time algorithm for the treasure hunt problem, which significantly improves the currently best known result of running time O(n) in [10], where c is a constant induced from the construction of an universal exploration sequence in [9, 10], and λ ≫ 1 is an arbitrary large, but fixed, integer constant. The treasure hunt problem also motivates the study of strongly universal exploration sequences. In this paper, we also propose a much better explicit construction for strongly universal exploration sequences compared to the one in [10].