Before revision:  We first design a deterministic treasure hunt algorithm working in the model without any restrictions on the moves of the agent at cost O(e(d) \log d), and then show how to modify this algorithm to work in the model from [ ABRS 1999 ] with the same complexity.
After revision:  We first design a deterministic treasure hunt algorithm working in the model without any restrictions on the moves of the agent at cost O(e(d) \log d), and then show how to modify this algorithm to work in the model from [ 3 ] with the same complexity.