Efficient suffix trees on secondary storage
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Orderly spanning trees with applications to graph encoding and graph drawing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Journal of Algorithms
Succinct representations of lcp information and improvements in the compressed suffix arrays
SODA '02 Proceedings of the thirteenth 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
Succinct Representation of Balanced Parentheses and Static Trees
SIAM Journal on Computing
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Representing Trees of Higer Degree
WADS '99 Proceedings of the 6th International Workshop on Algorithms and 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
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
On searching compressed string collections cache-obliviously
Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
A Uniform Approach Towards Succinct Representation of Trees
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
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
Compact navigation and distance oracles for graphs with small treewidth
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Succinct representations of permutations and functions
Theoretical Computer Science
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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Various methods have been used to represent a tree of n nodes in essentially the information-theoretic minimum space while supporting various navigational operations in constant time, but different representations usually support different operations. Our main contribution is a succinct representation of ordinal trees, based on that of Geary et al. (7), that supports all the navigational operations supported by various succinct tree representations while requiring only 2n + o(n) bits. It also supports efficient level-order traversal, a useful ordering previously supported only with a very limited set of operations (8). Our second contribution expands on the notion of a single succinct representation supporting more than one traversal ordering, by showing that our method supports two other encoding schemes as abstract data types. In particular, it supports extracting a word (O(lg n) bits) of the balanced parenthesis sequence (11) or depth first unary degree sequence (3; 4) in O(f(n)) time, using at most n/f(n) +o(n) additional bits, for any f(n) in O(lg n) and Ω(1).