Revisiting Local Computation of PageRank: Simple and Optimal

We revisit ApproxContributions, the classic local graph exploration algorithm proposed by Andersen, Borgs, Chayes, Hopcroft, Mirrokni, and Teng (WAW '07, Internet Math. '08) for computing an є-approximation of the PageRank contribution vector for a target node t on a graph with n nodes and m edges. We give a worst-case complexity bound of it as O(nπ(t)/є·min(Δin,Δout,√m)), where π(t) is the PageRank score of t, and Δin and Δout are the maximum in-degree and out-degree of the graph, resp. We also give a lower bound of Ω(min(Δin/δ,Δout/δ,√m/δ,m)) for detecting t's δ-contributing set, showing that the simple ApproxContributions algorithm is already optimal.