Journal ArticleDOI
Succinct ordinal trees based on tree covering
TLDR
A succinct representation of ordinal trees, based on that of Geary et al.Abstract:
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).read more
Citations
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Journal ArticleDOI
Fully Functional Static and Dynamic Succinct Trees
TL;DR: The range min-max tree as discussed by the authors is a data structure for ordinal trees that can be represented in 2n p O(n/polylog(n)) bits of space.
Proceedings Article
Succinct trees in practice
TL;DR: The latter technique stands out as an excellent practical combination of space occupancy, time performance, and functionality, whereas others, particularly LOUDS, are still interesting in some limited-functionality niches.
Posted Content
Succinct Representations of Permutations and Functions
TL;DR: The redundancy of one of the structures ''surpasses'' a recent lower bound by Golynski [Golynski, SODA 2009], thus demonstrating the limitations of this lower bound.
Book ChapterDOI
Succinct representations of binary trees for range minimum queries
TL;DR: Two succinct representations of binary trees that can be used to represent the Cartesian tree of an array A of size n are provided and it is shown that the pre-processing needed to output the data structure can be performed in linear time using o(n) bits of extra working space.
Book ChapterDOI
The Function-Inversion Problem: Barriers and Opportunities
TL;DR: Oechslin et al. as discussed by the authors showed that it is possible to invert a random function in time (T = \widetilde{O}(N^{2/3}) given only bits of precomputed advice about f.
References
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Book ChapterDOI
The LCA Problem Revisited
TL;DR: A very simple algorithm for the Least Common Ancestors problem is presented, dispelling the frequently held notion that optimal LCA computation is unwieldy and unimplementable.
Proceedings ArticleDOI
Space-efficient static trees and graphs
TL;DR: Data structures that represent static unlabeled trees and planar graphs are developed, and there is no other structure that encodes n-node trees with fewer bits per node, as N grows without bound.
Journal ArticleDOI
A unified approach to visibility representations of planar graphs
TL;DR: This work studies visibility representations of graphs, which are constructed by mapping vertices to horizontal segments, and edges to vertical segments that intersect only adjacent vertex-segments, and considers three types of visibility representations.
Journal ArticleDOI
Succinct indexable dictionaries with applications to encoding k-ary trees, prefix sums and multisets
TL;DR: In the cell probe model, the O(lg lg m) additive term can be removed from the space bound, answering a question raised by Fich and Miltersen [1995] and Pagh [2001].
Journal ArticleDOI
Succinct Representation of Balanced Parentheses and Static Trees
J. Ian Munro,Venkatesh Raman +1 more
TL;DR: This work considers the implementation of abstract data types for the static objects: binary tree, rooted ordered tree, and a balanced sequence of parentheses to produce a succinct representation of planar graphs in which one can test adjacency in constant time.
Related Papers (5)
Succinct ordinal trees with level-ancestor queries
Succinct Representation of Balanced Parentheses and Static Trees
J. Ian Munro,Venkatesh Raman +1 more