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About this paper
Jun-Ting Hsieh, Pravesh K. Kothari, Sidhanth Mohanty
This paper by Hsieh, Kothari, and Mohanty dramatically simplifies and strengthens the proof of the hypergraph Moore bound, establishing a nearly tight bound with only a single logarithmic factor loss. Their reweighted Kikuchi matrix and targeted edge deletion techniques lead to a more precise characterization and yield improved algorithms for constraint satisfaction problem refutation.
Key insights
- The reweighted Kikuchi matrix simplifies spectral analysis by inherently handling vertex degree irregularities, eliminating complex combinatorial bucketing.
- A targeted edge deletion process for odd uniformity hypergraphs maintains structural integrity while removing only a small fraction of 'bad' edges, leading to cleaner proofs.
- The techniques based on spectral analysis of auxiliary graphs (Kikuchi graphs) and trace moment method provide a unified framework for both even and odd uniformities.
Summary by alphaXiv.
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