Faster Treasure Hunt and Better Strongly Universal Exploration Sequences

Abstract

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 $O(n^{c(1+\frac{1}{\lambda})})$-time solution for this problem, which significantly improves the currently best known result of running time O(n ^2c) 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].