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The Arborescence-Sampling Barrier for Eulerian Tours

Sampling a nearly uniform Eulerian tour of a directed Eulerian multigraph was stuck at $mn$-type running times coming from arborescence sampling. A randomized algorithm achieves $\widetilde{O}(m^{3/2})$ worst case, breaking that barrier on sparse graphs.

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Occurred: May 28, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.

Canonical aliases: The Arborescence-Sampling Barrier for Eulerian Tours · Eulerian tour sampling

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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VibeMathed
registry · event recorded by

Nima Anari
human · human collaborator

GPT-5.5 Pro Extended
model · ai model contributor · OpenAI

Codex
model · ai model contributor · OpenAI

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This event attributed to Nima Anari

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This event attributed to GPT-5.5 Pro Extended

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