Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Finding level-ancestors in trees
Journal of Computer and System Sciences
Efficient suffix trees on secondary storage
Proceedings of the seventh 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
The Level Ancestor Problem Simplified
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Perfect Hashing for Strings: Formalization and Algorithms
CPM '96 Proceedings of the 7th Annual Symposium on Combinatorial Pattern Matching
Orderly Spanning Trees with Applications
SIAM Journal on Computing
Structuring labeled trees for optimal succinctness, and beyond
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Representing Trees of Higher Degree
Algorithmica
Succinct indexable dictionaries with applications to encoding k-ary trees, prefix sums and multisets
ACM Transactions on Algorithms (TALG)
On the Redundancy of Succinct Data Structures
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
A Uniform Approach Towards Succinct Representation of Trees
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Succinct representations of planar maps
Theoretical Computer Science
Succinct geometric indexes supporting point location queries
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
On the bit-complexity of Lempel-Ziv compression
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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
Succinct Orthogonal Range Search Structures on a Grid with Applications to Text Indexing
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Compressing and indexing labeled trees, with applications
Journal of the ACM (JACM)
A Compressed Enhanced Suffix Array Supporting Fast String Matching
SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
Note: Combined data structure for previous- and next-smaller-values
Theoretical Computer Science
Succinct representation of dynamic trees
Theoretical Computer Science
Succinct indexes for strings, binary relations and multilabeled trees
ACM Transactions on Algorithms (TALG)
A compact encoding of unordered binary trees
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Ultra-succinct representation of ordered trees with applications
Journal of Computer and System Sciences
Succinct geometric indexes supporting point location queries
ACM Transactions on Algorithms (TALG)
Bounding the number of reduced trees, cographs, and series-parallel graphs by compression
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Path queries in weighted trees
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Succinct representations of permutations and functions
Theoretical Computer Science
Succinct ordinal trees based on tree covering
ACM Transactions on Algorithms (TALG)
Dynamizing succinct tree representations
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
Succinct ordinal trees based on tree covering
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Succinct data structures for path queries
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We consider succinct or space-efficient representations of trees that efficiently support a variety of navigation operations. We focus on static ordinal trees, that is, arbitrary static rooted trees where the children of each node are ordered. The set of operations is essentially the union of the sets of operations supported by previous succinct representations [Jacobson 1989; Munro and Raman 2001; Benoit et al. 1999] to which we add the level-ancestor operation.Our representation takes 2n + o(n) bits to represent an n-node tree, which is within o(n) bits of the information-theoretic minimum, and supports all operations in O(1) time on the RAM model. These operations also provide a mapping from the n nodes of the tree onto the integers {1, …, n}. In addition to the existing motivations for studying such data structures, we are motivated by the problem of representing XML documents compactly so that XPath queries can be supported efficiently.