On the CGGRT Criterion for Detecting Bipartite Perfect Matchings in NC

Swastik Kopparty; Shubhangi Saraf

On the CGGRT Criterion for Detecting Bipartite Perfect Matchings in NC

Computational Complexity 2026-07-17 v1 Data Structures and Algorithms Combinatorics

Authors: Swastik Kopparty , Shubhangi Saraf

Abstract

The recent breakthrough work of Chatterjee, Ghosh, Gurjar, Raj and Thierauf [CGGRT26] gives the first deterministic NC algorithm for the bipartite matching problem. They show how to detect as well as find perfect matchings in bipartite graphs in NC. In this note we present an arguably simpler-to-state variation of the NC detection criterion of [CGGRT26], with improved parameters.

Keywords

bipartite perfect matching NC algorithm deterministic algorithm CGGRT criterion complexity theory

Cite

@article{arxiv.2607.15554,
  title  = {On the CGGRT Criterion for Detecting Bipartite Perfect Matchings in NC},
  author = {Swastik Kopparty and Shubhangi Saraf},
  journal= {arXiv preprint arXiv:2607.15554},
  year   = {2026}
}

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8 pages