Sorting shuffled monotone sequences
Information and Computation
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
High-order entropy-compressed text indexes
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Representing Trees of Higher Degree
Algorithmica
Squeezing succinct data structures into entropy bounds
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
ACM Computing Surveys (CSUR)
The cell probe complexity of succinct data structures
Theoretical Computer Science
Ultra-succinct representation of ordered trees
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Succinct indexes for strings, binary relations and multi-labeled 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)
Optimal lower bounds for rank and select indexes
Theoretical Computer Science
Practical Entropy-Bounded Schemes for O(1)-Range Minimum Queries
DCC '08 Proceedings of the Data Compression Conference
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Sorting and selection in posets
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Faster entropy-bounded compressed suffix trees
Theoretical Computer Science
Lowest common ancestors in trees and directed acyclic graphs
Journal of Algorithms
Succinct representations of permutations
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Implicit compression boosting with applications to self-indexing
SPIRE'07 Proceedings of the 14th international conference on String processing and information retrieval
Fully-functional succinct trees
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On space efficient two dimensional range minimum data structures
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Optimal succinctness for range minimum queries
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
On the range maximum-sum segment query problem
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to index integer arrays in order to support range minimum queries on them. We describe how they yield many other convenient results in a variety of areas: compressed succinct indices for range minimum queries on partially sorted arrays; a new adaptive sorting algorithm; and a compressed succinct data structure for permutations supporting direct and inverse application in time inversely proportional to the permutation's compressibility.