Tighter Lower Bounds for Single Source Personalized PageRank

We study lower bounds for approximating the Single Source Personalized PageRank (SSPPR) query, which measures the probability distribution of an $α$-decay random walk starting from a source node $s$. Existing lower bounds remain loose-$Ω\left(\min(m, 1/δ)\right)$ for relative error (SSPPR-R) and $Ω\left(\min(n, 1/ε)\right)$ for additive error (SSPPR-A). To close this gap, we establish tighter bounds for both settings. For SSPPR-R, we show a lower bound of $Ω\left(\min\left(m, \frac{\log(1/δ)}δ\right)\right)$ for any $δ\in (0,1)$. For SSPPR-A, we prove a lower bound of $Ω\left(\min\left(m, \frac{\log(1/ε)}ε\right)\right)$ for any $ε\in (0,1)$, assuming the graph has $m \in \mathcal{O}(n^{2-β})$ edges for any arbitrarily small constant $β\in (0,1)$.