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  "path": "/abs/2606.24421v1",
  "publishedAt": "2026-06-24T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Minghao Chen",
    "Jiale Zheng"
  ],
  "textContent": "**Authors:** Minghao Chen, Jiale Zheng\n\nSpectral filtering recently delivered substantial pruning for \\emph{static} subgraph matching: Laplacian interlacing rejects candidates whose neighborhoods cannot host the query. We study whether such aggregate structural tests can accelerate \\emph{continuous} subgraph matching (CSM) over dynamic graphs, and answer in three parts. First, lazily maintained spectral bounds are infeasible exactly where spectral pruning has value: we characterize the tightest safe rule over a formalized perturbation relaxation and show that even it loses essentially all pruning power within four touching updates. Second, exact maintenance is affordable when selective: pruning utility and recomputation cost are anti-correlated across vertices -- hubs provably never prune -- so recomputing small-neighborhood spectra on touch sustains exact local spectra at microseconds per update, complete by construction. Third, integrated into a decoupled CSM benchmark against an identical-minus-spectra control, the tests remove up to $51\\%$ of candidates or safely skip up to $47\\%$ of update enumerations, yet enumeration intermediates remain unchanged -- beyond the gates' skipped first-level bindings, typically zero -- across two engines, four real graphs, two stream types, and $77$ solved queries; a constructed radius-stratified workload confirms the instrument detects the exception when one exists ($-99.9\\%$ intermediates, $748\\times$ faster). Aggregate tests accelerate what scales with candidate sets -- construction, list scans -- never adjacency-guided exploration. We distill an intermediate-invariance methodology for evaluating CSM filters and release a reusable dynamic local-spectra index.",
  "title": "Can Aggregate Invariants Accelerate Continuous Subgraph Matching? Limits, Laws, and a Dynamic Spectral Index"
}