A Succinct Data Structure for Multidimensional Orthogonal Range Searching

2017 ◽  
Author(s):  
Kazuki Ishiyama ◽  
Kunihiko Sadakane
Keyword(s):  
Data Structure ◽  
Range Searching ◽  
Succinct Data Structure ◽  
Orthogonal Range Searching

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 Multivariate Analysis of Orthogonal Range Searching and Graph Distances

Algorithmica ◽  
2020 ◽  
Vol 82 (8) ◽  
pp. 2292-2315
Author(s):  
Karl Bringmann ◽  
Thore Husfeldt ◽  
Måns Magnusson
Keyword(s):  
Multivariate Analysis ◽  
Range Searching ◽  
Orthogonal Range Searching ◽  
Graph Distances
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