The cell probe complexity of dynamic data structures
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Efficient suffix trees on secondary storage
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Representing dynamic binary trees succinctly
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Succinct representation of balanced parentheses, static trees and planar graphs
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Representing Trees of Higher Degree
Algorithmica
Succinct ordinal trees with level-ancestor queries
ACM Transactions on Algorithms (TALG)
Compressed indexes for dynamic text collections
ACM Transactions on Algorithms (TALG)
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
An Improved Succinct Representation for Dynamic k-ary Trees
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
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
A framework for dynamizing succinct data structures
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
An empirical evaluation of extendible arrays
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
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We study the problem of maintaining a dynamic tree succinctly, in 2n + o (n ) bits, under updates of the following form: insertion or deletion of a leaf, insertion of a node on an edge (edge subdivision) or deletion of a node with only one child (the child becomes a child of the grandparent). We allow satellite data of a fixed (but not necessarily constant) size to be associated to the nodes of the tree. We support update operations in constant amortized time and support access to satellite data and basic navigation operations in worst-case constant time; the basic navigation operations includes parent , first/last-child , previous/next-child . We demonstrate that to allow fast support for more extended operations such as determining the i -th child of a node, rank of a child among its siblings, or subtree size, we require a restrictive update strategy for which we propose the finger-update model where updates are performed by a finger which is only allowed to crawl on the tree (between a child and a parent or between consecutive siblings). Under this model, we describe how the named operations can be performed in worst-case constant time. Previous work on dynamic succinct ordered trees [1,2] is mainly restricted to binary trees and achieves poly-logarithmic [1] or "poly-log-log" [2] update time under a more restricted model. Best previous result on ordinal trees achieves only sublinear amortized update time and "poly-log-log" query time [3].