Before revision:  We also confirm this result analytically. Moreover the algorithm is implemented without the need for a specific oracle step, but by topological hole defect in the grid. From a quantum computing perspective, however, this hints at novel applications of quantum walk search: instead of using them to look for "good" solutions within the configuration space of a problem, we could use them to look for topological properties of the entire configuration space .
After revision:  We also proved that there exists an optimal choice of the walker parameters to avoid that the time measurement precision affects the complexity searching time of the algorithm .