To run eclipse from on remote ubuntu 13.10 server using x11 on local machine.
Prerequisites: I am assuming JDK and Eclipse is already installed.
In addition to that you need to install few libraries on remote server. Run the following command to install those libraries on remote server.
$ sudo apt-get install libgtk2.0-0:i386 libxxf86vm1:i386 libsm6:i386 lib32stdc++6 libxtst6
Once above libraries are install open another terminal and connect remote server through ssh with -X option
#From local machine
$ ssh <username>@<remote machine ip> -X
Now you can start the eclipse from this ssh session
#From local machine
$ cd <to location where eclipse is installed>
$ ./eclipse