Static Data Structure Lower Bounds Imply Rigidity

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A formal connection proves that hard linear static data-structure problems correspond to rigid matrices by relating outer dimension (data-structure complexity) to inner dimension (row-rigidity): a large outer dimension implies a small inner dimension up to a logarithmic sparsity loss. The proof gives a PNP procedure that recursively extracts a rigid submatrix (losing a log factor), and uses linear LDCs to boost worst-case rigidity to average-case. Corollary: any super‑logarithmic query lower bound against 1.01n space yields new rigidity bounds.

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1. 0:00Intro
2. 0:45Data Structure
3. 3:53Cell Probe Model
4. 7:32Nonadaptive Data Structures
5. 10:07Linear Data Structures
6. 13:40PolyLogarithmic
7. 17:15Linear Data Structure
8. 19:50Matrix rigidity
9. 24:13Motivation
10. 28:36rigidity
11. 31:25Semantic differences
12. 35:55Property of a matrix
13. 45:31Submatrix
14. 58:23LDC