Monte Carlo Methods in PageRank Computation: When One Iteration is Sufficient
SIAM Journal on Numerical Analysis
Fast incremental and personalized PageRank
Proceedings of the VLDB Endowment
| Hi-index | 0.89 |
This note extends the analysis of incremental PageRank in Bahmani et al. (2010) [1]. In that work, the authors prove a running time of O(nR@e^2ln(m)) to keep PageRank updated over m edge arrivals in a graph with n nodes when the algorithm stores R random walks per node and the PageRank teleport probability is @e. To prove this running time, they assume that edges arrive in a random order, and leave it to future work to extend their running time guarantees to adversarial edge arrival. In this note, we show that the random edge order assumption is necessary by exhibiting a graph and adversarial edge arrival order in which the running time is @W(Rnm^l^g^3^2^(^1^-^@e^)). More generally, for any integer d=2, we construct a graph and adversarial edge order in which the running time is @W(Rnm^l^o^g^"^d^(^H^"^d^(^1^-^@e^)^)), where H"d is the dth harmonic number.