Основные понятия
Revisiting the complexity of ApproxContributions and BiPPR algorithms for efficient PageRank estimation.
Аннотация
The content discusses the ApproxContributions algorithm for computing PageRank contributions and its worst-case complexity bounds. It also introduces the BiPPR algorithm, a combination of ApproxContributions and Monte Carlo simulation, for single-node PageRank estimation. The analysis provides insights into the computational complexities and variance of estimators in these algorithms.
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ApproxContributions Algorithm:
- Introduced by Andersen et al. for computing PageRank contributions.
- Worst-case complexity bound: O(nπ(t)/ϵ · min(∆in, ∆out, √m)).
- Applications in estimating random-walk probabilities.
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BiPPR Algorithm:
- Combines ApproxContributions with Monte Carlo simulation.
- Computes a multiplicative (1±c)-approximation of π(t) w.p. at least (1−pf).
- Expected computational complexity: O(nπ(t)/ϵ · min(∆in, ∆out, √m) + nr).
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Variance Analysis:
- Variance of estimator ˆπ(t) in BiPPR is bounded by ϵnr · π(t).
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Median Trick Optimization:
- Boosts success probability to (1-pf) using reruns and median trick.
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Simplicity vs Complexity:
- Comparison with previous complex analyses highlights simplicity in deriving tight upper bounds.
Статистика
We give a worst-case complexity bound of ApproxContributions as O(nπ(t)/ϵ · min(∆in, ∆out, √m)).
The expected computational complexity of running BiPPR is O(nπ(t)/ϵ · min(∆in, ∆out, √m) + nr).
Цитаты
"ApproxContributions has become a cornerstone for computing random-walk probabilities."
"Our results show that the simple ApproxContributions algorithm is already optimal."