$requested_start = ...;  # a value between 0 and 1
    $avg_line_len = ...;  # make a guess or read a small sample to estimate this

    $file_size = -s $filename;
    $read_length = $avg_line_len * 1000;
    seek( FH, $file_size * $requested_start, 0 );
    read( FH, $text, $read_length );

    $text =~ s/^.*\n//;  # trim initial and final
    $text =~ s/.*$//;    #   line fragments from $text