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About this paper
Yichun Yang, Rong-Hua Li, Meihao Liao, Guoren Wang
Researchers at the Beijing Institute of Technology developed improved algorithms for approximating Effective Resistance (ER) on graphs, significantly reducing the dependency on the approximation error parameter `ϵ` for both local online and index-based computation. Their work provides an `˜O(√d/ϵ)` local online algorithm, an `Ω(1/ϵ)` lower bound, and an ER sketch with `˜O(min{m + n/ϵ^(1.5), √nm/ϵ})` processing time, outperforming previous state-of-the-art methods.
Key insights
- A synergistic combination of deterministic search methods (CGD) and random walk sampling can effectively reduce variance and improve the `ϵ`-dependency for approximating spectral graph properties.
- The `Ω(1/ϵ)` lower bound proves that linear dependency on `1/ϵ` is the best achievable for local ER approximation on expander graphs, nearly closing the theoretical gap for this problem.
- The sparsity of `ϵ`-contributing sets for `pL,u` vectors allows for efficient structuring and sharing of computations, particularly in index-based algorithms, leading to improved preprocessing times.
Summary by alphaXiv.
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