scholarly journals A succinct data structure for self-indexing ternary relations

2017 ◽  
Vol 43 ◽  
pp. 38-53 ◽  
Author(s):  
Sandra Alvarez-Garcia ◽  
Guillermo de Bernardo ◽  
Nieves R. Brisaboa ◽  
Gonzalo Navarro
Keyword(s):  
Data Structure ◽  
Succinct Data Structure

scholarly journals DenseZDD: A Compact and Fast Index for Families of Sets

Algorithms ◽  
2018 ◽  
Vol 11 (8) ◽  
pp. 128 ◽  
Author(s):  
Shuhei Denzumi ◽  
Jun Kawahara ◽  
Koji Tsuda ◽  
Hiroki Arimura ◽  
Shin-ichi Minato ◽  
...  
Keyword(s):  
Data Structure ◽  
Data Structures ◽  
Information Integration ◽  
Decision Diagrams ◽  
Web Information Retrieval ◽  
Binary Decision ◽  
Web Information ◽  
Set Operations ◽  
Succinct Data Structure ◽  
The Family

In this article, we propose a succinct data structure of zero-suppressed binary decision diagrams (ZDDs). A ZDD represents sets of combinations efficiently and we can perform various set operations on the ZDD without explicitly extracting combinations. Thanks to these features, ZDDs have been applied to web information retrieval, information integration, and data mining. However, to support rich manipulation of sets of combinations and update ZDDs in the future, ZDDs need too much space, which means that there is still room to be compressed. The paper introduces a new succinct data structure, called DenseZDD, for further compressing a ZDD when we do not need to conduct set operations on the ZDD but want to examine whether a given set is included in the family represented by the ZDD, and count the number of elements in the family. We also propose a hybrid method, which combines DenseZDDs with ordinary ZDDs. By numerical experiments, we show that the sizes of our data structures are three times smaller than those of ordinary ZDDs, and membership operations and random sampling on DenseZDDs are about ten times and three times faster than those on ordinary ZDDs for some datasets, respectively.

scholarly journals Metannot: A succinct data structure for compression of colors in dynamic de Bruijn graphs

2017 ◽  
Author(s):  
Harun Mustafa ◽  
André Kahles ◽  
Mikhail Karasikov ◽  
Gunnar Rätsch
Keyword(s):  
Data Structure ◽  
High Throughput Sequencing ◽  
Sequence Data ◽  
Data Sets ◽  
Sequencing Data ◽  
Dynamic Data ◽  
De Bruijn Graphs ◽  
Dna And Rna ◽  
Succinct Data Structure ◽  
Dynamic Data Structure

AbstractMuch of the DNA and RNA sequencing data available is in the form of high-throughput sequencing (HTS) reads and is currently unindexed by established sequence search databases. Recent succinct data structures for indexing both reference sequences and HTS data, along with associated metadata, have been based on either hashing or graph models, but many of these structures are static in nature, and thus, not well-suited as backends for dynamic databases.We propose a parallel construction method for and novel application of the wavelet trie as a dynamic data structure for compressing and indexing graph metadata. By developing an algorithm for merging wavelet tries, we are able to construct large tries in parallel by merging smaller tries constructed concurrently from batches of data.When compared against general compression algorithms and those developed specifically for graph colors (VARI and Rainbowfish), our method achieves compression ratios superior to gzip and VARI, converging to compression ratios of 6.5% to 2% on data sets constructed from over 600 virus genomes.While marginally worse than compression by bzip2 or Rainbowfish, this structure allows for both fast extension and query. We also found that additionally encoding graph topology metadata improved compression ratios, particularly on data sets consisting of several mutually-exclusive reference genomes.It was also observed that the compression ratio of wavelet tries grew sublinearly with the density of the annotation matrices.This work is a significant step towards implementing a dynamic data structure for indexing large annotated sequence data sets that supports fast query and update operations. At the time of writing, no established standard tool has filled this niche.

scholarly journals Succinct Encoding of Binary Strings Representing Triangulations

Algorithmica ◽  
2021 ◽  
Author(s):  
José Fuentes-Sepúlveda ◽  
Diego Seco ◽  
Raquel Viaña
Keyword(s):  
Information Theory ◽  
Data Structure ◽  
Experimental Evaluation ◽  
Special Class ◽  
Spanning Trees ◽  
State Of The Art ◽  
Succinct Data Structure ◽  
Planar Embeddings ◽  
Specific Sequences ◽  
Binary Strings

AbstractWe consider the problem of designing a succinct data structure for representing the connectivity of planar triangulations. The main result is a new succinct encoding achieving the information-theory optimal bound of 3.24 bits per vertex, while allowing efficient navigation. Our representation is based on the bijection of Poulalhon and Schaeffer (Algorithmica, 46(3):505–527, 2006) that defines a mapping between planar triangulations and a special class of spanning trees, called PS-trees. The proposed solution differs from previous approaches in that operations in planar triangulations are reduced to operations in particular parentheses sequences encoding PS-trees. Existing methods to handle balanced parentheses sequences have to be combined and extended to operate on such specific sequences, essentially for retrieving matching elements. The new encoding supports extracting the d neighbors of a query vertex in O(d) time and testing adjacency between two vertices in O(1) time. Additionally, we provide an implementation of our proposed data structure. In the experimental evaluation, our representation reaches up to 7.35 bits per vertex, improving the space usage of state-of-the-art implementations for planar embeddings.

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