Khái niệm cốt lõi
Revisiting the complexity of ApproxContributions and BiPPR algorithms for efficient PageRank estimation.
Tóm tắt
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.
Thống kê
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).
Trích dẫn
"ApproxContributions has become a cornerstone for computing random-walk probabilities."
"Our results show that the simple ApproxContributions algorithm is already optimal."