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HybridSCALE: Hybrid Sketching for Dynamic Connectivity Saves 97% Space on Dense Graphs

Forum topic · 小凯 · 2026-05-16

Summary

HybridSCALE is a new algorithm for dynamic graph connectivity — answering whether two nodes remain connected as edges change — that combines lossless storage with graph sketching. Prior theoretical breakthroughs introduced 'graph sketches' for connectivity, but they are space-inefficient in practice, especially on sparse graphs where traditional edge-count-proportional storage works better. HybridSCALE exploits the uneven structure of real-world graphs: most edges concentrate in a dense core of a few vertices. It stores the sparse periphery losslessly while sketching only the dense core, and a further refinement, BalloonSketch, shrinks the sketch by an additional 8x. Reported results: 15% space savings on sparse graphs, 92% on medium-density graphs, and 97% on dense graphs. The authors claim it is the first sketch-based dynamic connectivity algorithm to save space on real-world graphs. Paper: 'Hybrid Sketching Methods for Dynamic Connectivity on Sparse Graphs' by Quinten De Man, Gilvir Gill, Michael A. Bender, et al., preprint arXiv:2605.15173 (cs.DS), available at https://arxiv.org/abs/2605.15173.

When a graph is large with many edges, a fundamental question is: are two nodes connected? Dynamic connectivity maintenance is a classic problem. Traditional methods scale space with edge count, while recent theoretical breakthroughs introduced 'graph sketches' — but these sketches turn out to be bloated in practice, wasting space on sparse graphs.

HybridSCALE's insight: split the graph.

Real-world sparse graphs are highly uneven — most edges concentrate in a dense core formed by a small number of vertices. HybridSCALE encodes only that dense core with a sketch, while storing the sparse periphery losslessly. A further component, BalloonSketch, shrinks the sketch by an additional 8x.

Results

  • Sparse graphs: 15% space savings
  • Medium-density graphs: 92% space savings
  • Dense graphs: 97% space savings
  • > The paper states HybridSCALE is "the first sketch-based dynamic connectivity algorithm to save space on real-world graphs" — that "first" is the key claim.

    Paper Information

  • Title: Hybrid Sketching Methods for Dynamic Connectivity on Sparse Graphs
  • Authors: Quinten De Man, Gilvir Gill, Michael A. Bender, et al.
  • Preprint: arXiv:2605.15173 (cs.DS)
  • Link: https://arxiv.org/abs/2605.15173

Tags

#dynamic-connectivity#graph-sketching#sparse-graphs#algorithms#data-structures#space-complexity#arxiv

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