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.
Liu and Richard Peng and Aaron Sidford , editor =
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A bidirectional reduction between suffix random access and function inversion enables improved asymmetric streaming algorithms for exact/approximate pattern matching and relative Lempel-Ziv compression.
A dynamic parallel constant-time LCE algorithm uses a string synchronizing sets hierarchy to handle updates with O(n^ε) work and enables constant-time maintenance for Dyck language membership and square detection.
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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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Suffix Random Access via Function Inversion: A Key for Asymmetric Streaming String Algorithms
A bidirectional reduction between suffix random access and function inversion enables improved asymmetric streaming algorithms for exact/approximate pattern matching and relative Lempel-Ziv compression.
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Longest Common Extension of a Dynamic String in Parallel Constant Time
A dynamic parallel constant-time LCE algorithm uses a string synchronizing sets hierarchy to handle updates with O(n^ε) work and enables constant-time maintenance for Dyck language membership and square detection.