Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
PATRICIA—Practical Algorithm To Retrieve Information Coded in Alphanumeric
Journal of the ACM (JACM)
A Space-Economical Suffix Tree Construction Algorithm
Journal of the ACM (JACM)
Journal of Algorithms
Time-space trade-offs for compressed suffix arrays
Information Processing Letters
Succinct indexable dictionaries with applications to encoding k-ary trees and multisets
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Low Redundancy in Static Dictionaries with Constant Query Time
SIAM Journal on Computing
Succinct Representation of Balanced Parentheses and Static Trees
SIAM Journal on Computing
High-order entropy-compressed text indexes
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the 16th Conference on Foundations of Software Technology and Theoretical Computer Science
New text indexing functionalities of the compressed suffix arrays
Journal of Algorithms
Orderly Spanning Trees with Applications
SIAM Journal on Computing
Journal of the ACM (JACM)
Compressed Suffix Arrays and Suffix Trees with Applications to Text Indexing and String Matching
SIAM Journal on Computing
Representing Trees of Higher Degree
Algorithmica
Squeezing succinct data structures into entropy bounds
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Succinct ordinal trees with level-ancestor queries
ACM Transactions on Algorithms (TALG)
A simple optimal representation for balanced parentheses
Theoretical Computer Science
Note: A simple storage scheme for strings achieving entropy bounds
Theoretical Computer Science
Ultra-succinct representation of ordered trees
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Compressed Suffix Trees with Full Functionality
Theory of Computing Systems
Balanced parentheses strike back
ACM Transactions on Algorithms (TALG)
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
A Uniform Approach Towards Succinct Representation of Trees
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Linear pattern matching algorithms
SWAT '73 Proceedings of the 14th Annual Symposium on Switching and Automata Theory (swat 1973)
Universal Succinct Representations of Trees?
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Compressing and indexing labeled trees, with applications
Journal of the ACM (JACM)
Fully-functional succinct trees
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Opportunistic data structures for range queries
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Succinct ordinal trees based on tree covering
ACM Transactions on Algorithms (TALG)
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There exist two well-known succinct representations of ordered trees: BP (balanced parenthesis) (Munro and Raman, 2001) [20] and DFUDS (depth first unary degree sequence) (Benoit et al., 2005) [1]. Both have size 2n+o(n) bits for n-node trees, which asymptotically matches the information-theoretic lower bound. Importantly, many fundamental operations on trees can be done in constant time on the word RAM when using BP or DFUDS, for example finding the parent, the first child, the next sibling, the number of descendants, etc. Although the space needed to store the BP or DFUDS representation of an ordered tree matches the lower bound, this is not optimal when we consider encodings for certain special classes of trees such as trees in which every internal node has exactly two children. In this paper, we introduce a new, conditional entropy for trees called the tree degree entropy, and give a succinct tree representation with matching size. We call such a representation an ultra-succinct data structure. We show how to modify the DFUDS representation to obtain a ''compressed DFUDS'', and as a consequence, a tree in which every internal node has exactly two children can be represented in n+o(n) bits. We also describe applications of the compressed DFUDS representation to ultra-succinct compressed suffix trees and labeled trees.