Computer Science Seminar
Date: Friday, 1 August 2025
Time: 2:00 PM
Venue: Online
Bipartite Matching is in Catalytic Logspace
Aryan Agarwala
Max Planck Institute.
01-08-25

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Abstract

Matching is a central problem in theoretical computer science, with a large body of work spanning the last five decades. However, understanding matching in the time-space bounded setting remains a longstanding open question, even in the presence of additional resources such as randomness or non-determinism.

In this work we study space-bounded machines with access to catalytic space, which is additional working memory that is full with arbitrary data that must be preserved at the end of its computation. Despite this heavy restriction, many recent works have shown the power of catalytic space, its utility in designing classical space-bounded algorithms, and surprising connections between catalytic computation and derandomization.

Our main result is that bipartite maximum matching (MATCH) can be computed in catalytic logspace (CL) with a polynomial time bound (CLP). Moreover, we show that MATCH can be reduced to the lossy coding problem for NC circuits (LOSSY[NC]). This has consequences for matching, catalytic space, and derandomization.

This is joint work with Ian Mertz.