Random Walks with Look-ahead in Scale-free Random Graphs

If m ≥ 2 is constant and 0 ≤ r ≤ ε log log n for a small positive constant ε, then whp a random walk with look-ahead r on a scale-free graph G = G(m,n) has cover time C_G(r) ∼ (2/(m^r−1 (m − 1))) n log n.