# Revisiting Local Computation of PageRank: Simple and Optimal

arXiv: https://arxiv.org/abs/2403.12648 · HTML: https://mlsanity.com/paper/2403.12648/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2024.

## Built on by (most cited first, 2 of 2)

- [Local Clustering on Complex Graphs and Complex Hypergraphs](https://mlsanity.com/paper/2412.03008/) (2024)
- [Accelerated Evolving Set Processes for Local PageRank Computation](https://mlsanity.com/paper/2510.08010/) (2025)

## Abstract (arXiv)

We revisit the classic local graph exploration algorithm ApproxContributions proposed by Andersen, Borgs, Chayes, Hopcroft, Mirrokni, and Teng (WAW '07, Internet Math. '08) for computing an ε-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 ApproxContributions as O(nπ(t)/ε·min(Deltain,Deltaout,√m)), where π(t) is the PageRank score of t, and Deltain and Deltaout are the maximum in-degree and out-degree of the graph, resp. We also give a lower bound of Omega(min(Deltain/δ,Deltaout/δ,√m/δ,m)) for detecting the δ-contributing set of t, showing that the simple ApproxContributions algorithm is already optimal. We also investigate the computational complexity of locally estimating a node's PageRank centrality. We improve the best-known upper bound of widetildeO(n2/3·min(Deltaout1/3,m1/6)) given by Bressan, Peserico, and Pretto (SICOMP '23) to O(n1/2·min(Deltain1/2,Deltaout1/2,m1/4)) by simply combining ApproxContributions with the Monte Carlo simulation method. We also improve their lower bound of Omega(min(n1/2Deltaout1/2,n1/3m1/3)) to Omega(n1/2·min(Deltain1/2,Deltaout1/2,m1/4)) if min(Deltain,Deltaout)=Omega(n1/3), and to Omega(n1/2-γ(min(Deltain,Deltaout))1/2+γ) if min(Deltain,Deltaout)=o(n1/3), where γ>0 is an arbitrarily small constant. Our matching upper and lower bounds resolve the open problem of whether one can tighten the bounds given by Bressan, Peserico, and Pretto (FOCS '18, SICOMP '23). Remarkably, the techniques and analyses for proving all our results are surprisingly simple.