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

Outline 2

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

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

Memory Model

Ordinal Trees 6 x a b c

Ordinal Tree Representations 7

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Previous Results 10

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

Hardness of Arbitrary Updates 12

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

Previous Results 14 amortized

Our Result 15

Data Structure 16

Main Contribution 17

Open Problems 18

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