1. Succinct Dynamic Cardinal Trees with Constant Time Operations for Small Alphabet Pooya Davoodi Aarhus University May 24, 2011 S. Srinivasa Rao Seoul National University

2. Outline 2

3. Succinct Data Structures  Goal: – Represent data in close to optimal space (optimal: information-theoretic lower bound) – Support operations efficiently  Example: succinct representation of trees 3 Compress but also preserve accessibility and functionality

4. Motivation for Succinct Trees  Directories (Unix, all the rest)  Search trees (B-trees, binary search trees, digital trees, or tries)  Graph structures (doing a tree based search)  Search indexes for text (including DNA) – Suffix trees  XML documents  … 4

5. Memory Model

6. Ordinal Trees 6 x a b c

7. Ordinal Tree Representations 7

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9. 9

10. Previous Results 10

11. Dynamic Cardinal Trees  Data structures support the update operations: – Inserting a leaf – Deleting a leaf 11 “Data optimization is much easier when we can sit back and do it off-line.” Jocobson, 1989

12. Hardness of Arbitrary Updates 12

13. Traversal Model  A traversal starts and ends at the root  Queries and updates are performed at the current node of the traversal 13

14. Previous Results 14 amortized

15. Our Result 15

16. Data Structure 16

17. Main Contribution 17

18. Open Problems 18

19. Thank You