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.
Subquadratic Algorithm for Dynamic Shortest Distances , booktitle =
3 Pith papers cite this work, alongside 5 external citations. Polarity classification is still indexing.
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Computing GapMAJ∘fⁿ requires n·(I−O(1)) bits of information, making GapMAJ the third outer gadget with a strong composition theorem in two-player communication.
The 4x4 Klein bottle grid graph has 192 C4-face-magic labelings up to symmetries, classified by whether they admit horizontally or vertically pairwise balanced permutations.
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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.
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Gap-Majority Lemmas in Communication Complexity
Computing GapMAJ∘fⁿ requires n·(I−O(1)) bits of information, making GapMAJ the third outer gadget with a strong composition theorem in two-player communication.
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C4-face-magic labeling on a 4x4 Klein bottle grid graph
The 4x4 Klein bottle grid graph has 192 C4-face-magic labelings up to symmetries, classified by whether they admit horizontally or vertically pairwise balanced permutations.