In theory this means that powering from a plain old USB port will not do. For my initial tests I used a 2 amp "Samsung" branded wall module intended for my cell phone that was laying around and it seemed to work just fine.
However, subsequent to that first checkout, I have been powering the board from an ordinary USB cable plugged into a random port on my desktop PC. A port like this should be limited to 500 mA. I have had no problems, even booting and running linux. I expect though that if I started doing real computations and getting all 8 cores busy things would not be good.
Giving this a bit of thought, consider this. This chip has 8 cores. If only one is busy, one might guess it would draw 2/8 = 250 mA, which would be entirely reasonable for a 500 mA USB port.
A person could consider a fancy heat sink pad. A recommended brand and type is the "Thermal Grizzly Minus Pad 8". Amazon sells this in a 120x20x1.0mm strip for $12. The supplied pad is 16x16x2mm. This nicely covers the entire s5p6818 chip, not just the central die section.
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