Ropebwt3 introduces a faster algorithm for long sequences and retains the same ropebwt2 algorithm as an alternative (invoked with ropebwt3 build -2). It also has additional functionality.

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Introduction

RopeBWT2 is an tool for constructing the FM-index for a collection of DNA sequences. It works by incrementally inserting one or multiple sequences into an existing pseudo-BWT position by position, starting from the end of the sequences. This algorithm can be largely considered a mixture of BCR and dynamic FM-index. Nonetheless, ropeBWT2 is unique in that it may implicitly sort the input into reverse lexicographical order (RLO) or reverse-complement lexicographical order (RCLO) while building the index. Suppose we have file seq.txt in the one-sequence-per-line format. RLO can be achieved with Unix commands:

rev seq.txt | sort | rev

RopeBWT2 is able to perform sorting together with the construction of the FM-index. As such, the following command lines give the same output:

shuf seq.txt | ropebwt2 -LRs | md5sum
rev seq.txt | sort | rev | ropebwt2 -LR | md5sum

Here option -s enables the RLO mode. Similarly, the following command lines give the same output (option -r enables RCLO):

shuf seq.txt | ropebwt2 -LRr
rev seq.txt | tr "ACGT" "TGCA" | sort | tr "ACGT" "TGCA" | rev | ropebwt2 -LR

RLO/RCLO has two benefits. Firstly, such ordering clusters sequences with similar suffixes and helps to improve the compressibility especially for short reads (Cox et al, 2012). Secondly, when we put both forward and reverse complement sequences in RCLO, the resulting index has a nice feature: the reverse complement of the k-th sequence in the FM-index is the k-th smallest sequence. This would eliminate an array to map the rank of a sequence to its index in the input. This array is usually not compressible unless the input is sorted.

RopeBWT2 is developed for indexing hundreds of billions of symbols. It has been carefully optimized for both speed and memory usage. On a new machine with Xeon E5-2697v2 CPUs at 2.70GHz, ropeBWT2 is able to the index for 1.2 billion 101bp reads in five wall-clock hours with 34G peak memory.

If you use RopeBWT2 or its predecessor RopeBWT in your work, please cite:

Li H (2014) Fast construction of FM-index for long sequence reads, Bioinformatics, 30:3274-5. [PMID: 25107872]

Examples

1. Construct the BWT for sequences in the input order:

    ropebwt2 -o out.bwt in.fa
   

2. Construct the BWT for sequences in RLO and output the BWT in the ropebwt2 binary format:

    ropebwt2 -bso out.fmr in.fa
   

3. Construct the BWT for sequences in RLO, processing 4GB symbols at a time with multithreading:

    ropebwt2 -brm4g in.fa > out.fmr
   

   Note that for sequence reads, processing multiple sequences together is faster due to possible multi-threading and fewer cache misses. The peak memory is about B+m*(1+48/l), where B is the size of the final BWT encoded in a B+-tree, m is the parameter value of '-m' and l is the average read length.

4. Add sequences to an existing index with the sorting order defined by the existing index (incremental construction):

    ropebwt2 -bi in.fmr in.fa > out.fmr
   

Methods Overview

RopeBWT2 keeps the entire BWT in six B+ trees with the i-th tree storing the substring B[C(i)+1..C(i+1)], where C(i) equals the number of symbols lexicographically smaller than i. In each B+ tree, an internal node keeps the count of symbols in the subtree descending from it; an external node keeps a BWT substring in the run-length encoding. The B+ tree achieve a similar purpose to the rope data structure, which enables efficient query and insertion. RopeBWT2 uses this rope-like data structure to achieve incremental construction. This is where word 'rope' in ropeBWT2 comes from.

The original BCR implementation uses static encoding to keep BWT. Although it is possible to insert strings to an existing BWT, we have to read through the old BWT. Reading the entire BWT may be much slower than the actual insertion. With the rope data structure, we can insert one or many sequences of length m in O(mlogn) time without reading all the BWT. We can thus achieve efficient incremental construction.

To achieve RLO for one-string insertion, we insert the symbol that is ahead of a suffix at the position based on the rank of the suffix computed from backward search. Inserting multiple strings in RLO is essentially a combination of radix sort, BCR and single-string insertion. RopeBWT2 uses radix sort to group symbols with an identical suffix, compute the rank of the suffix with backward search and insert the group of symbols based on the BCR theory. For RCLO, we find the insertion points with the complemented sequence but insert with the original string.

RopeBWT2 vs. ropeBWT

RopeBWT is the predecessor of ropeBWT2. The old version implements three separate algorithms: in-memory BCR, single-string incremental FM-index on top of a B+ tree and single-string incremental FM-index on top of a red-black tree. BCR is later extended to support RLO and RCLO as well.

The BCR implementation in ropeBWT is the fastest so far for short reads, faster than ropeBWT2. The legacy BCR implementation is still the preferred choice for constructing the FM-index of short reads for the assembly purpose. However, with parallelized incremental multi-string insertion, ropeBWT2 is faster than ropeBWT for incremental index construction and works much better with long strings. RopeBWT2 also uses more advanced run-length encoding, which will be more space efficient for highly repetitive inputs and opens the possibility for inserting a run in addition individual symbols.

RopeBWT2 vs. BEETL

BEETL is the original implementation of the BCR algorithm. It uses disk to alleviate the memory requirement for constructing large FM-index and therefore heavily relies on fast linear disk access. BEETL supports the SAP order for inserting sequences but not RLO or RCLO.

RopeBWT2 vs. dynamic FM-index

RopeBWT was conceived in 2012, but the algorithm has been invented several years earlier for multiple times. Dynamic FM-index is a notable implementation that uses a wavelet tree for generic text and supports the deletion operation. As it is not specifically designed for DNA sequences, it is apparently ten times slower and uses more memory on the index construction.

Performance Evaluation

Data sets

1. [worm] 66,764,080 100bp C. elegans reads from SRR065390 with pairs containing any ambiguous bases filtered out. The total coverage is about 66X.

2. [Venter] 31,861,134 Craig Venter reads totalled in 27,899,994,048bp. Reads containing ambiguous bases have been dropped.

3. [NA12878] 1,206,555,986 101bp human reads for sample NA12878, used in my fermi paper. Pairs containing ambiguous bases are filtered out. The data is at 1000g FTP. Only read groups matching "20FUK" are used.

4. [Moleculo] 22,721,139 Moleculo reads totalled in 91,476,572,938bp. This data set contains a few hundred ambiguous bases which are not filtered.

Hardware and OS

CPU: 48 cores of Xeon E5-2697 v2 at 2.70GHz. GPU: one Nvidia Tesla K40. RAM: 128GB. OS: Red Hat Enterprise Linux 6. CUDA: 5.5. File system: Isilon OneFS network file system.

Results

Dataset	w/ rev	Algorithm	Sorted	CPU	Real	RSS	Comment
worm	No	BEETL-BCR	-	2574s	2092s	1.8G	network disk
worm	No	BEETL-BCR	-	2497s	965s	1.8G	RAM disk
worm	No	BEETL-BCRext	-	2839s	5900s	12.6M	network disk
worm	No	nvSetBWT	-	484s	416s	10.9G	mem: 2g/4g
worm	No	nvSetBWT	-	435s	316s	12.9G	mem: 4g/4g
worm	No	nvSetBWT	-	434s	309s	24.9G	mem: 16g/4g
worm	No	nvSetBWT	-	499s	480s	21.5G	mem: 16g/2g
worm	No	ropebwt-BCR	No	1070s	480s	2.2G	-bORtf -abcr
worm	No	ropebwt-bpr	-	4279s	4296s	2.3G	-bOR
worm	No	ropebwt-rbr	-	8895s	8915s	2.3G	-bOR -arbr
worm	No	ropebwt2-single	No	5105s	5125s	2.5G	-bRm0
worm	No	ropebwt2	No	1611s	647s	11.8G	-bRm10g
worm	No	ropebwt2	Yes	1268s	506s	10.5G	-brRm10g
worm	Yes	ropebwt2	No	3566s	1384s	18.0G	-bm10g
worm	Yes	ropebwt2	Yes	3116s	1182s	15.9G	-brm10g
NA12878	No	BEETL-BCR	-	14.66h	11.18h	31.6G	network disk
NA12878	No	nvSetBWT	-	19.33h	4.10h	63.8G	mem: 48g/4g
NA12878	No	ropebwt-BCR	No	6.92h	3.29h	39.3G	-bORtf -abcr
NA12878	No	ropebwt2	No	12.54h	5.06h	60.9G	-bRm10g
NA12878	No	ropebwt2	Yes	12.94h	4.96h	34.0G	-brRm10g
Venter	No	ropebwt2	No	3.98h	1.45h	22.8G	-bRm10g
Venter	No	ropebwt2	Yes	3.95h	1.44h	22.2G	-brRm10g
Moleculo	No	ropebwt2	No	19.46h	6.82h	20.0G	-bRm10g

• For ropebwt and ropebwt2, outputting the BWT to a plain text string takes significant time. We let them dump the BWT in their internal binary encoding. BEETL automatically chooses the RLE encoding in our evaluation. Changing the BEETL encoding may also affect its performance.

• nvSetBWT from NVBio aborted when '-gpu-mem 6144' or higher is specified. It seems that nvSetBWT uses more GPU memory than -gpu-mem according to the nvidia-smi report. nvSetBWT failed to build the index for Venter apparently due to insufficient RAM.