The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Compact pat trees
Efficient suffix trees on secondary storage
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Catalan, Motzkin, and Riordan numbers
Discrete Mathematics - Special issue on selected papers in honor of Henry W. Gould
Representing dynamic binary trees succinctly
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
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
Concrete Mathematics: A Foundation for Computer Science
Concrete Mathematics: A Foundation for Computer Science
Succinct representation of balanced parentheses, static trees and planar graphs
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Succinct static data structures
Succinct static data structures
Representing Trees of Higher Degree
Algorithmica
Succinct ordinal trees with level-ancestor queries
ACM Transactions on Algorithms (TALG)
Ultra-succinct representation of ordered trees
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Succinct indexes for strings, binary relations and multi-labeled trees
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Succinct ordinal trees based on tree covering
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Dynamic Succinct Ordered Trees
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Universal Succinct Representations of Trees?
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Fully-functional succinct trees
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Note: Combined data structure for previous- and next-smaller-values
Theoretical Computer Science
Succinct representation of dynamic trees
Theoretical Computer Science
Ultra-succinct representation of ordered trees with applications
Journal of Computer and System Sciences
Encoding 2d range maximum queries
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Succinct ordinal trees based on tree covering
ACM Transactions on Algorithms (TALG)
Succinct data structures for path queries
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We propose a uniform approach for succinct representation of various families of trees. The method is based on two recursive decomposition of trees into subtrees. Recursive decomposition of a structure into substructures is a common technique in succinct data structures and has been shown fruitful in succinct representation of ordinal trees [7,10] and dynamic binary trees [16,21]. We take an approach that simplifies the existing representation of ordinal trees while allowing the full set of navigational operations. The approach applied to cardinal (i.e. k-ary) trees yields a space-optimal succinct representation allowing cardinal-type operations (e.g. determining child labeled i) as well as the full set of ordinal-type operations (e.g. reporting the number of siblings to the left of a node). Existing space-optimal succinct representations had not been able to support both types of operations [2,19].We demonstrate how the approach can be applied to obtain a space-optimal succinct representation for the family of free trees where the order of children is insignificant. Furthermore, we show that our approach can be used to obtain entropy-based succinct representations. We show that our approach matches the degree-distribution entropy suggested by Jansson etal. [13]. We discuss that our approach can be made adaptive to various other entropy measures.