Representing dynamic binary trees succinctly
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Concrete Mathematics: A Foundation for Computer Science
Concrete Mathematics: A Foundation for Computer Science
Compact Encodings of Planar Graphs via Canonical Orderings and Multiple Parentheses
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
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
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 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 indexable dictionaries with applications to encoding k-ary trees, prefix sums and multisets
ACM Transactions on Algorithms (TALG)
EDBT '08 Proceedings of the 11th international conference on Extending database technology: Advances in database technology
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
Succinct dynamic dictionaries and trees
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Succinct ordinal trees based on tree covering
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Succinct dynamic cardinal trees with constant time operations for small alphabet
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 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 consider the succinct representation of ordinal and cardinal trees on the RAM with logarithmic word size. Given a tree T , our representations support the following operations in O (1) time: (i) $\mbox{{\tt BP-substring}}(i,b)$, which reports the substring of length b bits (b is at most the wordsize) beginning at position i of the balanced parenthesis representation of T , (ii) $\mbox{{\tt DFUDS-substring}}(i,b)$, which does the same for the depth first unary degree sequence representation, and (iii) a similar operation for tree-partition based representations of T . We give: an asymptotically space-optimal 2n + o (n ) bit representation of n -node ordinal trees that supports all the above operations with b = *** (logn ), answering an open question from [He et al., ICALP'07]. an asymptotically space-optimal C (n ,k ) + o (n )-bit representation of k -ary cardinal trees, that supports (with $b = \Theta(\sqrt{\log n})$) the operations (ii) and (iii) above, on the ordinal tree obtained by removing labels from the cardinal tree, as well as the usual label-based operations. As a result, we obtain a fully-functional cardinal tree representation with the above space complexity. This answers an open question from [Raman et al, SODA'02]. Our new representations are able to simultaneously emulate the BP, DFUDS and partitioned representations using a single instance of the data structure, and thus aim towards universality . They not only support the union of all the ordinal tree operations supported by these representations, but will also automatically inherit any new operations supported by these representations in the future.