Is there a way to miniaturize cell-phone power adapter
Is there a way to miniaturize a cell-phone power adapter to be not bigger than 1-3 cubic centimeters? ... -> 110 AC to 5V 1 A DC.


Apart from the mechanical and connector issues, yes, it is possible to make the devices smaller. 

Will it be expensive? oh yes!
 For a space mission this is a "just do it" requirement.
 For a consumer device, if you have to ask the price you can't afford one.
 [But, if you order 10,000 and pay in advance, I'll happily provide them for a few hundred dollars each]. 

The single most obvious method is to increase the frequency used by the SMPS (switched mode power supply. At present typical modern devices use frequencies from high 100's of kHz to low MHz range. By increasing rhe frequency to 10's of Mhz the inductances needed in transformers become utterly minimal and inductor size is a non issue. 

You are then faced with actually making a device work efficiently at these frequencies and accommodating the electronics required in the available volume.   

Making it work is "just a matter of engineering" [tm] :-). ie given enough $ you can provide devices capable of minimal switching losses at far higher frequencies. Synchronous rectification and resonant techniques and ... .   

Component size is also not a major issue. One IC of minimal size, a few power devices (MOSFETS probably for switching an rectification) with the inductors already a non issue size wise. Noise filtering is at the multi MHz range so also small. 

For 5V, 1A = 5W output and say even only 80% efficient
overall heat dissipation required =  5W x 0.2/0.8
 = 1.25W
 = acceptable for a device of that size given the right outer housing.     

At 90% you need 550 mW heat dissipation.