Scenario in PHP

"This summer you plan to go traveling around the world. You are lucky to have 32 friends
around the globe who will host and help you. Given a list of your
friends' GPS locations, write a script that will help you find the shortest path to visit all 32 of
your friends once."

Input file specifications
The input file will contain a listing of cities and coordinates in a tab-delimited file
The filename is named exactly "cities.txt"
Your script will assume this file is located on the same directory where the script is executed
There are no additional spaces or lines at the begging or end of the file
The list will being in "Beijing", you must begin your route there

The schema for this file is as follows:
<city name> \t <latitude> \t <longitude> \n

an example input file:
Beijing 39.93 116.40
Vladivostok 43.8 131.54
Dakar 14.40 -17.28
Singapore 1.14 103.55
(...)

Script and Runtime Specifications
You must submit exactly 1 PHP file called "solve.php"
Begin and end this file with the standard <?php ?> tags
The file must use Unix line endings
You will have access to all the standard PHP functions available in version 5.2.12
The max memory your script can use is 128 megabytes
The maximum execution time is 5 minutes

Output
Your script's final (and only) output will be using the standard "print()" function
Do not attempt to write to disk, only print to screen
The output must consist of a list of the 32 original cities provided in the input file "cities.txt"
These 32 cities should be ordered in the exact order in which you will visit your friends
There must be only one city name (exact spelling) per line followed by a newline delimeter
(\n)
You will be judged on the total distance covered in your travels, the shorter the better
You cannot visit a city twice, and you must visit all cities

The schema for your output print should be:
<city name> \n

Example output print:
Beijing
Vladivostok
Dakar
Singapore