The first dynamic algorithms for matrix rank and related objects achieve update times scaling with rank r, specifically Õ(r^1.405) per entry update and Õ(r^1.528 + z) per column update, extending to dynamic maximum matching.
A Deamortization Approach for Dynamic Spanner and Dynamic Maximal Matching , booktitle =
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Dynamic Rank, Basis, and Matching
The first dynamic algorithms for matrix rank and related objects achieve update times scaling with rank r, specifically Õ(r^1.405) per entry update and Õ(r^1.528 + z) per column update, extending to dynamic maximum matching.