Getting Started

# install and test
git clone https://github.com/lh3/miniwfa
cd miniwfa && make test-mwf
./test-mwf -c test/t3-?.fa

# use as a library
cp miniwfa.{c,h} kalloc.{c,h} your_src/

Introduction

Miniwfa is a reimplementation of the WaveFront Alignment algorithm (WFA) with dual gap penalty. For long diverged sequences, the original WFA is slow and memory hungry. Miniwfa introduces a low-memory mode and a chaining heuristic to address these issues.

Miniwfa was developed in parallel to the linear-space BiWFA algorithm. Now BiWFA uses less memory and is generally faster than miniwfa in the exact mode. Miniwfa is much faster in the heuristic mode but it does not guarantee to find the optimal solution.

Miniwfa can be used as a library. Here is a compilable sample program:

// compile with gcc -O3 this-prog.c miniwfa.c kalloc.c
#include <string.h>
#include <stdio.h>
#include "miniwfa.h"
int main(int argc, char *argv[]) {
  mwf_opt_t opt;
  mwf_rst_t r;
  mwf_opt_init(&opt);
  if (argc >= 3) {
    mwf_wfa_auto(0, &opt, strlen(argv[1]), argv[1], strlen(argv[2]), argv[2], &r);
    printf("%d\n", r.s);
  }
  return 0;
}

Algorithm

When reporting alignment score only, miniwfa behaves largely the same as the original WFA. Miniwfa differs mainly in traceback. In the high memory mode, miniwfa packs traceback information into 7 bits per entry:

extD2<<6 | extI2<<5 | extD1<<4 | extI1<<3 | fromState

where extD1, for example, indicates whether we are extending the D1 deletion state, and fromState keeps the max state (5 possible values). As such, miniwfa uses 1 byte for each traceback entry. The standard WFA uses 20 bytes per entry.

Miniwfa has a low-memory mode inspired by but different from wfalm. In the wfalm terminology, miniwfa stores a "stripe" of traceback information every p cycles. It finds the positions on these stripes that the optimal alignment path goes through. Miniwfa then applies the WFA algorithm for a second time. In this round, it resets the bandwidth to 1 whenever it reaches a stripe. Miniwfa approximately uses (20qs²/p+ps) bytes of memory. Here, s is the optimal alignment penalty, p is the distance between stripes and q=max(x,o₁+e₁,o₂+e₂) is the maximal penalty between adjacent entries. The time complexity is O(n(s+p)) where n is the length of the longer sequence.

In the heuristic mode, miniwfa chains low-occurrence k-mers and fills gaps in the chain with the exact algorithm.

Vectorization

Miniwfa relies on compiler vectorization to parallelize three key loops. Old compilers (e.g. gcc-4.8.5) that do not support auto vectorization will lead to lower performance. Some compilers (e.g. gcc-6.4.0) cannot vectorize one of the loops. Clang-13.1.6 and gcc-10.3.0 are known to work well with miniwfa. Also note that gcc does not vectorize loops with -O2 and vectorization is influenced by SIMD. If you use miniwfa as a library, it is recommended to enable -msse4 -O3 when compiling with gcc.

Evaluation

We only use three pairs of sequences for evaluation. The first pair consists of the two haplotypes of NA19240 around the C4A/C4B gene. They are 100-150kb in length with a penalty of 26,917 under penalty x=4, o₁=4, e₁=2, o₂=15 and e₂=1. The second pair consists of GRCh38 and CHM13 around MHC. They are about 5Mb in length with a penalty of 229,868. The third pair consists of the two MHC haplotypes in HG002 with a penalty of 267,637. These sequences can be found via Zenodo.

We checked out the development branch of WFA2-lib on 2022-04-25 and compiled the code with gcc-10.3.0 (no LTO) on a CentOS 7 server equipped with two Xeon 6230 CPUs. The table below shows the timing and peak memory for miniwfa and BiWFA in its linear mode. The table used to include other memory modes of WFA2-lib and wfalm, which were removed because BiWFA is a clear winner now.

Historical notes on WFA and related algorithms

I got the following notes wrong a few times. Please let me know if you found the narrative is still inaccurate.

Given a pair of strings, let n be the length of the longer string and d is the edit distance between the two strings. Ukkonen found the O(nd) algorithm to compute edit distances in 1983 and published it in 1985. Myers independently conceived the same algorithm in 1984 and published it in 1986. He additionally introduced a few variations including a linear-space algorithm with forward and reverse search. It is essentially BiWFA under edit distance. The idea of "wave" was implicit in Myers' 1986 paper. His 2014 paper explicitly explained "wave".

Sometimes the O(nd) algorithm is also attributed to Landau and Vishkin (1989). I don't know if Landau and Vishkin were aware of Ukkonen's work at the time of submission in 1986, but their published paper in 1989 did cite Ukkonen (1985).

The search for a similar algorithm for linear or affine gap penalties took three decades. To the best of my knowledge, Xin et al (2017) first found a version of this algorithm but apparently they have never published it in a peer-reviewed journal. Marco-Sola et al (2021) were probably unaware of Xin et al. They independently published the WFA algorithm as we know today. They also gave a highly efficient implementation, beating all global alignment algorithms by a large margin.

A major concern with the original WFA is its large memory consumption. Eizenga and Paten (2022) implemented wfalm to reduce its peak memory. This repo was inspired by this work. Then Marco-Sola et al (2022) developed BiWFA that finds the alignment in linear space. This is so far the best performing algorithm.

It is worth noting that also in 1985, Ukkonen published another algorithm with expected O(nt) time complexity where t is a given threshold. This algorithm guarantees to find the edit distance d if d≤t. It is somewhat similar to banded alignment but distinct from his O(nd) algorithm published in the same year.