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Breakthrough Tracker record

A preprint claims the optimal strong matroid secretary guarantee

Huang claims an expected-polynomial-time ordinal algorithm that is 1/e-probability-competitive for every matroid using only comparison and independence oracles on arrived elements.

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Stable ID
cs-strong-matroid-secretary-conjecture-2026
Revision
cs-strong-matroid-secretary-conjecture-2026.v1
Field
Theoretical computer science · Online algorithms, matroids and mechanism design
Evidence
Tier 1 · Peer reviewed: No
Record state
Provisional · Provisional claimed proof
Last checked

AI role

Huang reports extensive ChatGPT 6 Astra interaction with human guidance and verification. The contemporaneous contextual papers also disclose substantive AI assistance.

Record details

Problem or result
The strong matroid secretary conjecture in the ordinal oracle model
Authors
Zhiyi Huang; contextual results by Sahil Singla, Abdi and collaborators, and Bérczi and collaborators
Institutions
University of Hong Kong and collaborating institutions
Result date
Primary preprint submitted September 24, 2026

Why it matters

The claim upgrades a nearly two-decade-old constant-factor conjecture to the optimal classical secretary constant in the strongest common information model.

Limits

The surrounding papers establish important weaker or linear-matroid results but do not verify the all-matroid 1/e theorem. No peer review or formal artifact was located.

Sources

  1. Primary: Huang, strong matroid secretary conjecture
  2. Context: Singla, a 1/4 result for general matroids
  3. Context: Abdi et al., a 1/e result for linear matroids
  4. Context: Bérczi et al., concurrent linear-matroid result

Correction and revision history

  1. 2026-10-02 — Added after primary-source, scope, status, AI-role and limitation review.

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