Deterministic rendezvous, treasure hunts and strongly universal exploration sequences

We obtain several improved solutions for the deterministic rendezvous problem in general undirected graphs. Our solutions answer several problems left open in a recent paper by Dessmark et al. We also introduce an interesting variant of the rendezvous problem which we call the deterministic treasure hunt problem. Both the rendezvous and the treasure hunt problems motivate the study of universal traversal sequences and universal exploration sequences with some strengthened properties. We call such sequences strongly universal traversal (exploration) sequences. We give an explicit construction of strongly universal exploration sequences. The existence of strongly universal traversal sequences, as well as the solution of the most difficult variant of the deterministic treasure hunt problem, are left as intriguing open problems.

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