Extend the CLP framework beyond bipartite matching

Develop catalytic logspace with polynomial time (CLP) algorithms for problems strictly harder than bipartite maximum matching by extending the Agarwala–Mertz (2025) compress-or-random catalytic space framework used to place bipartite matching in CLP.

Background

Agarwala and Mertz (2025) showed that bipartite maximum matching lies in CLP, marking the first nontrivial problem outside TC^1 shown to be in CL. They posed the challenge of extending their catalytic framework to more difficult problems.

This paper advances that agenda by placing linear matroid intersection in CLP, but the broader task of extending the framework to additional, harder problems remains stated as an open direction.