Efficient suffix trees on secondary storage
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Journal of 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
Orderly Spanning Trees with Applications
SIAM Journal on Computing
Representing Trees of Higher Degree
Algorithmica
Succinct ordinal trees with level-ancestor queries
ACM Transactions on Algorithms (TALG)
Succinct indexable dictionaries with applications to encoding k-ary trees, prefix sums and multisets
ACM Transactions on Algorithms (TALG)
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
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
Succinct indexes for strings, binary relations and multilabeled trees
ACM Transactions on Algorithms (TALG)
Ultra-succinct representation of ordered trees with applications
Journal of Computer and System Sciences
Succinct ordinal trees based on tree covering
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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Various methods have been used to represent a tree on 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. [2006], 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. 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 or depth first unary degree sequence 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).