Introduction

KSW2 is a library to align a pair of biological sequences based on dynamic programming (DP). So far it comes with global alignment and alignment extension (no local alignment yet) under an affine gap cost function: gapCost(k) = q+k*e, or a two-piece affine gap cost: gapCost2(k) = min{q+k*e, q2+k*e2}. For the latter cost function, if q+e<q2+e2 and e>e2, (q,e) is effectively applied to short gaps only, while (q2,e2) applied to gaps no shorter than ceil((q2-q)/(e-e2)-1). It helps to retain long gaps. The algorithm behind the two-piece cost is close to Gotoh (1990).

KSW2 supports fixed banding and optionally produces alignment paths (i.e. CIGARs) with gaps either left- or right-aligned. It provides implementations using SSE2 and SSE4.1 intrinsics based on Hajime Suzuki's diagonal formulation which enables 16-way SSE parallelization for the most part of the inner loop, regardless of the maximum score of the alignment.

KSW2 implements the Suzuki-Kasahara algorithm and is a component of minimap2. If you use KSW2 in your work, please cite:

• Suzuki, H. and Kasahara, M. (2018). Introducing difference recurrence relations for faster semi-global alignment of long sequences. BMC Bioinformatics, 19:45.
• Li, H (2018) Minimap2: pairwise alignment for nucleotide sequences. Bioinformatics, 34:3094-3100.

Usage

Each ksw2_*.c file implements a single function and is independent of each other. Here are brief descriptions about what each file implements:

• ksw2_gg.c: global alignment; Green's standard formulation
• ksw2_gg2.c: global alignment; Suzuki's diagonal formulation
• ksw2_gg2_sse.c: global alignment with SSE intrinsics; Suzuki's
• ksw2_extz.c: global and extension alignment; Green's formulation
• ksw2_extz2_sse.c: global and extension with SSE intrinsics; Suzuki's
• ksw2_extd.c: global and extension alignment, dual gap cost; Green's formulation
• ksw2_extd2_sse.c: global and extension, dual gap cost, with SSE intrinsics; Suzuki's

Users are encouraged to copy the header file ksw2.h and relevant ksw2_*.c file to their own source code trees. On x86 CPUs with SSE2 intrinsics, ksw2_extz2_sse.c is recommended in general. It supports global alignment, alignment extension with Z-drop, score-only alignment, global-only alignment and right-aligned CIGARs. ksw2_gg*.c are mostly for demonstration and comparison purposes. They are annotated with more comments and easier to understand than ksw2_ext*.c. Header file ksw2.h contains brief documentations. TeX file ksw2.tex gives brief derivation.

To compile the test program ksw-test, just type make. It takes the advantage of SSE4.1 when available. To compile with SSE2 only, use make sse2=1 instead. If you have installed parasail, use make parasail=prefix, where prefix points to the parasail install directory (e.g. /usr/local).

The following shows a complete example about how to use the library.

#include <string.h>
#include <stdio.h>
#include "ksw2.h"

void align(const char *tseq, const char *qseq, int sc_mch, int sc_mis, int gapo, int gape)
{
	int i, a = sc_mch, b = sc_mis < 0? sc_mis : -sc_mis; // a>0 and b<0
	int8_t mat[25] = { a,b,b,b,0, b,a,b,b,0, b,b,a,b,0, b,b,b,a,0, 0,0,0,0,0 };
	int tl = strlen(tseq), ql = strlen(qseq);
	uint8_t *ts, *qs, c[256];
	ksw_extz_t ez;

	memset(&ez, 0, sizeof(ksw_extz_t));
	memset(c, 4, 256);
	c['A'] = c['a'] = 0; c['C'] = c['c'] = 1;
	c['G'] = c['g'] = 2; c['T'] = c['t'] = 3; // build the encoding table
	ts = (uint8_t*)malloc(tl);
	qs = (uint8_t*)malloc(ql);
	for (i = 0; i < tl; ++i) ts[i] = c[(uint8_t)tseq[i]]; // encode to 0/1/2/3
	for (i = 0; i < ql; ++i) qs[i] = c[(uint8_t)qseq[i]];
	ksw_extz(0, ql, qs, tl, ts, 5, mat, gapo, gape, -1, -1, 0, &ez);
	for (i = 0; i < ez.n_cigar; ++i) // print CIGAR
		printf("%d%c", ez.cigar[i]>>4, "MID"[ez.cigar[i]&0xf]);
	putchar('\n');
	free(ez.cigar); free(ts); free(qs);
}

int main(int argc, char *argv[])
{
	align("ATAGCTAGCTAGCAT", "AGCTAcCGCAT", 1, -2, 2, 1);
	return 0;
}

Performance Analysis

The following table shows timing on two pairs of long sequences (both in the "test" directory).

Data set	Command line options	Time (s)	CIGAR	Ext	SIMD	Source
50k	-t gg -s	7.3	N	N	N	ksw2
	-t gg2 -s	19.8	N	N	N	ksw2
	-t extz -s	9.2	N	Y	N	ksw2
	-t ps_nw	9.8	N	N	N	parasail
	-t ps_nw_striped_sse2_128_32	2.9	N	N	SSE2	parasail
	-t ps_nw_striped_32	2.2	N	N	SSE4	parasail
	-t ps_nw_diag_32	3.0	N	N	SSE4	parasail
	-t ps_nw_scan_32	3.0	N	N	SSE4	parasail
	-t extz2_sse -sg	0.96	N	N	SSE2	ksw2
	-t extz2_sse -sg	0.84	N	N	SSE4	ksw2
	-t extz2_sse -s	3.0	N	Y	SSE2	ksw2
	-t extz2_sse -s	2.7	N	Y	SSE4	ksw2
16.5k	-t gg -s	0.84	N	N	N	ksw2
	-t gg	1.6	Y	N	N	ksw2
	-t gg2	3.3	Y	N	N	ksw2
	-t extz	2.0	Y	Y	N	ksw2
	-t extz2_sse	0.40	Y	Y	SSE4	ksw2
	-t extz2_sse -g	0.18	Y	N	SSE4	ksw2

The standard DP formulation is about twice as fast as Suzuki's diagonal formulation (-tgg vs -tgg2), but SSE-based diagonal formulation is several times faster than the standard DP. If we only want to compute one global alignment score, we can use 16-way parallelization in the entire inner loop. For extension alignment, though, we need to keep an array of 32-bit scores and have to use 4-way parallelization for part of the inner loop. This significantly reduces performance (-sg vs -s). KSW2 is faster than parasail partly because the former uses one score for all matches and another score for all mismatches. For diagonal formulations, vectorization is more complex given a generic scoring matrix.

It is possible to further accelerate global alignment with dynamic banding as is implemented in edlib. However, it is not as effective for extension alignment. Another idea is adaptive banding, which might be worth trying at some point.

Alternative Libraries

Library	CIGAR	Intra-seq	Affine-gap	Local	Global	Glocal	Extension
edlib	Yes	Yes	No	Very fast	Very fast	Very fast	N/A
KSW	Yes	Yes	Yes	Fast	Slow	N/A	Slow
KSW2	Yes	Yes	Yes/dual	N/A	Fast	N/A	Fast
libgaba	Yes	Yes	Yes	N/A?	N/A?	N/A?	Fast
libssa	No	No?	Yes	Fast	Fast	N/A	N/A
Opal	No	No	Yes	Fast	Fast	Fast	N/A
Parasail	No	Yes	Yes	Fast	Fast	Fast	N/A
SeqAn	Yes	Yes	Yes	Slow	Slow	Slow	N/A
SSW	Yes	Yes	Yes	Fast	N/A	N/A	N/A
SWIPE	Yes	No	Yes	Fast	N/A?	N/A?	N/A
SWPS3	No	Yes	Yes	Fast	N/A?	N/A	N/A