As a bioinformatician, how often have you found yourself staring at the screen waiting for grep to find a certain gene or chromosome-basepair location in a gargantuan vcf, bed or gwas file? And then realize you forgot adding a field delimiter to your pattern so your search included way too much results? Thats a problem I have wanted so solve for a long time.

Luckily, these files are usually sorted, which means we should be able to use a binary search! So thats what I wrote this weekend; a tool you can use to instantly find genomic regions in anything from vcfs, bed files, csv data, gwas to plink genetic statistics with a friendly user interface. As implementing a binary sort on a text file presented me with a lot of interesting challenges, skip below for some implementation details.

$ time grep -E '11 119[0-9]{3} ' data
--- 11:119854:T:G 11 119854 T G G T 623.98 0.02301 0 624 0 0 1.8438e-05 -0 0 0 0.011331 1.84374e-05
--- 11:119945:G:C 11 119945 G C C G 622.6 1.3961 0 623 1 0 0.0011187 -0 0 0 0.71666 0.00111868
10,98s (9,84s(u) + 1,14s(s) 4kb 33+1 ctx)

$ time python3 -f data --chr Chr --bp BP chr11:119500/1000
SNPID RSID Chr BP A_allele B_allele MinorAllele MajorAllele AA AB BB AA_calls AB_calls BB_calls MAF HWE missing missing_calls Info CAF
--- 11:119854:T:G 11 119854 T G G T 623.98 0.02301 0 624 0 0 1.8438e-05 -0 0 0 0.011331 1.84374e-05
--- 11:119945:G:C 11 119945 G C C G 622.6 1.3961 0 623 1 0 0.0011187 -0 0 0 0.71666 0.00111868
0,11s (0,08s(u) + 0,03s(s) 14kb 0+1 ctx)


Here are some interesting challenges and their solutions for searching in sorted files. These are all genetic data agnostic, so maybe they’ll be of use in other projects as well.

Reading between the lines

As we perform our binary search, we’ll jump from one file position to another, until we find the line matching the user’s query. These positions are most likely not at the start of a line. So we need some kind op method to read one or more lines given a position in the file. Why more than one line? Continue reading :)

def read_lines_at(f, pos, nlines=1, buffer_size=40960):
    '''reads <nlines> complete lines from binary stream f at pos.

    read_lines_at() searches for the first occurance of
    a newline, then proceeds from there by returning the
    next <nlines> complete lines. When (the nonnegative) <pos> is zero,
    the initial search is skipped.
    All lines must be contained in a read of <buffer_size> from pos.
    If this does not fit, the function fails.
    If EOF is found as the last line, b'' is returned instead (like at EOF). Another read after that would result in failure.

    read_lines_at() returns a tuple (position of line start, [lines]).
    On failure, (_, None) is returned.
    lines = []
    data =
    if data:
        s = data.find(b'\n')+1 if pos > 0 else 0
        if s == 0 and pos != 0 and len(data) == buffer_size:
            # buffer size is not large enough
            return -1, None
        line_start = pos + s
        e = s
        for idx in range(nlines):
            e = data.find(b'\n', s)
            if e == -1:
                if idx < nlines - 1:
                    return line_start, None
                e = None
            if e is not None:
                s = e + 1
        return line_start, lines
        return pos, None

Binary search in a text file

Next up, our binary search itself! Remember, normally we start in the middle of a sorted array. There, we compare our query item with that element, and then either perform the algorithm on the region below or above the middle, or our element is the right element and we return its index. However, region queries usually turn up much more than one index. So we need to find the leftmost match for our query, and then just read lines until the query does not match anymore.

To make a binary search find this leftmost line, we need to look at two lines at the same time. Then the ‘element’ our algorithm is looking for, are the two consecutive lines where the first line does not match the query, and the second line does. This combined with some logic for the first and last lines, I ended up with:

def search_left(f, seek_from, seek_to, value, keyf):
    '''finds the first line for which keyf(at, line) == value.'''
    a, b = seek_from, seek_to
    while a != b:
        pos = (a + b) // 2
        line_start, (left, right) = read_lines_at(f, pos, nlines=2)
        left_value = keyf(line_start, left) if left else None
        right_value = keyf(line_start, right) if right else None
        if left_value != value and right_value == value:
            return line_start + len(left) + 1, right
        elif not right or right_value >= value:
            b = pos
        elif right_value < value:
            if a + 1 == b:
            a = pos
    if pos == 0:
        line_start, (first_line,) = read_lines_at(f, 0, 1)
        if keyf(line_start, first_line) == value:
            return 0, first_line
        return 0, None
    return seek_to - 1, None

While the lines within for a certain chromosome are usually sorted with respect to basepair position, the chromosomes themselves are not always sorted in a file. So you have to poke the file in a smart way until you find one occurancy of your query chromosome. Let’s call this the pivot line. Then you can define a complete order on the file by comparing a chromosome’s name with the query chromsome. If they are not equal, compare the line’s position with the position of the pivot line.

So what is a simple and reasonable smart way of poking our file? A breadth first search! Thinking of how to implement that on an array was a fun excercise, but ended up being quite simple. Performing it on a ‘array’ with indices continuous in the range 0-1, the traversal would follow: 1/2; 1/4, 3/4; 1/8, 3/8, 5/8, 7/8 etc.. Then the pattern is fairly obvious.

def bfs_indices(length, depth=None):
    '''generates linear breadth first search indices.

    Returns array indices as if a breadth first search
    is performed on a binary tree constructed from a
    sorted linear array of length <length>. Defaults
    to a search through the entire array, but early
    stopping is possible by providing the maximum
    tree search level <depth>.

    >>> list(linear_bfs_indices(length=10))
    [5, 2, 7, 1, 3, 6, 8, 0, 1, 3, 4, 5, 6, 8, 9]
    >>> list(linear_bfs_indices(length=512, depth=3))
    [256, 128, 384, 64, 192, 320, 448]
    >>> len(set(linear_bfs_indices(length=10)))
    denom = 2
    if depth is None:
        depth = length.bit_length()
    while depth != 0:
        for num in range(1, denom, 2):
            yield length * num // denom
        depth, denom = depth-1, denom*2

The curse of gzip compression

Still then, there is the annoying problem that all these neatly sorted files are usually compressed with gzip - which does not allow random access halfway the file in the general case. Thus searching can only be done by reading the file line by line, even though there are compression tools available like bgzip (or maybe dictzip or bzip2, see stackoverflow) that create a compressed file for which binary search would work perfectly, readable on all systems by default, with only slightly larger file sizes… bgzip is usually used for vcf and bed files together with tabix, but by itself it already provides enough information for fast searching.

I did some expriments that showed that with a lot of hard work random access to a gzip seems to be possible for files compressed with the default flags. Maybe there will be a post on that later.

Later: so I modified a public deflate implementation s.t. it would be able to start halfway a gzip file and continue reading from there, keeping track of known and unknown output characters. More general, it doesn’t only read gzip files, but any random container format containing DEFLATE compressed data. Under the constraint of only outputting printable ascii characters, we can recover data after starting randomly inside a DEFLATE stream. Sadly, this only works for files with very low complexity (like seq 1 100000), not for genetics files because gzip likes to create arbitrary long (~100 MB’s) backreferences in its output for neglible compression gains. Anyway, if you need a program that’s able to recover DEFLATE streams from unknown container files, it’s available here.