On the CGGRT Criterion for Detecting Bipartite Perfect Matchings in NC

2026-07-16

AI Summary

This work addresses the problem of efficiently determining whether a bipartite graph admits a perfect matching within the NC complexity class. Building upon the framework introduced by CGGRT26, we propose a simpler deterministic NC algorithm that leverages algebraic and combinatorial techniques to formulate a parallel decision criterion. Our approach not only streamlines the original theoretical framework but also achieves improved bounds on key parameters, thereby enhancing the theoretical parallel efficiency of detecting perfect matchings in bipartite graphs.

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.

Problem

• bipartite matching
• perfect matching
• NC algorithm
• deterministic detection
• graph matching

Innovation

• bipartite matching
• perfect matching
• NC algorithm
• deterministic algorithm
• CGGRT criterion