This may be very similar to the idea described by SuicideJunkie here... but in real Perl code!

#!/usr/bin/perl

use strict;
use warnings;
use 5.010;

my $len = 87688;

open my $rfh, '<', 'ranges.txt' or die $!;

my (@start, @end);

while (<$rfh>) {
    chomp;
    my ($start, $end) = split /\s+/;
    $start--; $end--;
    if ($start > $end) {
        my $start2 = $start - $len;
        push @start, ($start2 < -$end ? -$end : $start2);
        push @end, $end;

        $end += $len;
    }
    push @start, $start;
    push @end, $end;
}

# sort the ranges
my @ix = sort { $start[$a] <=> $start[$b]
                           or
                  $end[$b] <=> $end[$a]   } 0..$#start;

# filter out shadowed ranges
my @good;
my $last_end = -1;
for my $ix (@ix) {
    if ($end[$ix] > $last_end) {
        push @good, $ix;
        $last_end = $end[$ix];
    }
}

# create slopes
my @top;
my $last_ix = shift @good;
for my $ix (@good) {
    my $x0 = int (($start[$last_ix] + $end[$last_ix] + 1) / 2);
    my $y0 = $end[$last_ix] - $x0;
    my $x1 = int (($start[$ix] + $end[$ix]) / 2);
    my $y01 = $x0 - $start[$ix];
    $last_ix = $ix;
    for my $x ($x0..$x1) {
        $top[$x] = ($y0 > $y01 ? $y0 : $y01);
        $y0--;
        $y01++;
    }
}

$#top = $len - 1;

say $_ + 1 for @top;
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Note that it does not handle the case where there are points not covered by any range.