use strict;
use warnings;

my %buckets;
my $lineStart = tell DATA;

while (<DATA>) {
    chomp;
    next unless length;
    push @{$buckets{lc substr $_, 0, 1}}, [$lineStart, tell DATA];
    $lineStart = tell DATA;
}

for my $key (sort keys %buckets) {
    my @pairs = map {"@$_"} @{$buckets{$key}};
    print "$key: ", (join ', ', @pairs), "\n";
}

__DATA__
Ok, let's say file A has a series of strings, one per line. Let's say that file
B has a series of strings, one per line.

The goal is, for each line in A, to return the best match from B using a
subroutine named fuzzy_match, a function that takes two strings and returns a
float from 0 to 1.

Now, let's assume that file B is enormous, making the prospect of applying
fuzzy_match to each member infeasible. But let's also assume that the first
character of each member of B will always be the best result from fuzzy_match
for A. This means that instead of looking through all of B, you simply need to
retrieve all records from B which start with the same first letter as the
current record in A.