Collisions among random walks on a graph
SIAM Journal on Discrete Mathematics
Undirected ST-connectivity in log-space
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Asynchronous deterministic rendezvous in graphs
Theoretical Computer Science
Deterministic Rendezvous in Graphs
Algorithmica
Deterministic rendezvous, treasure hunts and strongly universal exploration sequences
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Random walks, universal traversal sequences, and the complexity of maze problems
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
How to meet in anonymous network
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Polynomial deterministic rendezvous in arbitrary graphs
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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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].