Revisiting Local PageRank Estimation on Undirected Graphs: Simple and Optimal
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909315147759616 |
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| author | Wang, Hanzhi |
| author_facet | Wang, Hanzhi |
| contents | We propose a simple and optimal algorithm, BackMC, for local PageRank estimation in undirected graphs: given an arbitrary target node $t$ in an undirected graph $G$ comprising $n$ nodes and $m$ edges, BackMC accurately estimates the PageRank score of node $t$ while assuring a small relative error and a high success probability. The worst-case computational complexity of BackMC is upper bounded by $O\left(\frac{1}{d_{\mathrm{min}}}\cdot \min\left(d_t, m^{1/2}\right)\right)$, where $d_{\mathrm{min}}$ denotes the minimum degree of $G$, and $d_t$ denotes the degree of $t$, respectively. Compared to the previously best upper bound of $ O\left(\log{n}\cdot \min\left(d_t, m^{1/2}\right)\right)$ (VLDB '23), which is derived from a significantly more complex algorithm and analysis, our BackMC improves the computational complexity for this problem by a factor of $Θ\left(\frac{\log{n}}{d_{\mathrm{min}}}\right)$ with a much simpler algorithm. Furthermore, we establish a matching lower bound of $Ω\left(\frac{1}{d_{\mathrm{min}}}\cdot \min\left(d_t, m^{1/2}\right)\right)$ for any algorithm that attempts to solve the problem of local PageRank estimation, demonstrating the theoretical optimality of our BackMC. We conduct extensive experiments on various large-scale real-world and synthetic graphs, where BackMC consistently shows superior performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08978 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revisiting Local PageRank Estimation on Undirected Graphs: Simple and Optimal Wang, Hanzhi Data Structures and Algorithms We propose a simple and optimal algorithm, BackMC, for local PageRank estimation in undirected graphs: given an arbitrary target node $t$ in an undirected graph $G$ comprising $n$ nodes and $m$ edges, BackMC accurately estimates the PageRank score of node $t$ while assuring a small relative error and a high success probability. The worst-case computational complexity of BackMC is upper bounded by $O\left(\frac{1}{d_{\mathrm{min}}}\cdot \min\left(d_t, m^{1/2}\right)\right)$, where $d_{\mathrm{min}}$ denotes the minimum degree of $G$, and $d_t$ denotes the degree of $t$, respectively. Compared to the previously best upper bound of $ O\left(\log{n}\cdot \min\left(d_t, m^{1/2}\right)\right)$ (VLDB '23), which is derived from a significantly more complex algorithm and analysis, our BackMC improves the computational complexity for this problem by a factor of $Θ\left(\frac{\log{n}}{d_{\mathrm{min}}}\right)$ with a much simpler algorithm. Furthermore, we establish a matching lower bound of $Ω\left(\frac{1}{d_{\mathrm{min}}}\cdot \min\left(d_t, m^{1/2}\right)\right)$ for any algorithm that attempts to solve the problem of local PageRank estimation, demonstrating the theoretical optimality of our BackMC. We conduct extensive experiments on various large-scale real-world and synthetic graphs, where BackMC consistently shows superior performance. |
| title | Revisiting Local PageRank Estimation on Undirected Graphs: Simple and Optimal |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2409.08978 |