Mobile peer-to-peer connections

I want to make some software that would be great if it do not needed a server at all.

It is possible to make an internet connection between two mobile devices?

Does someone have a clue on what I nee开发者_运维百科d to research for iPhone, Android and Blackberry?

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You can do a direct connection with UDP or TCP but you will encounter logistical problems. For example if you are on the same wifi network all will be good. But if one phone is on a wifi network with a NAT'd address and the other is on a public address, you will have problems since the private NAT'd address is not route-able. If the phone with the private knows the ip of the public address phone,the private ip phone can make the initial contact.
This is why people use server to have one central location for everyone to meet and connections can be established.