If you really want a positive displacement supercharger you're better off running it straight off the belt because a separate engine would be a lot of weight, and would probably lack in efficiency compared to the main engine anyways. Belt drive losses are very small, and the efficiency of a Roots blower depends a bit more on pressure ratio than speed.
If you want fancy ideas about using a Roots blower, some things to consider would be electric drive (so it can be operated in reverse for power generation off intake vacuum, but on a diesel this is not very useful), and a CVT connecting it to the crankshaft for direct boost control or the ability to recover throttling losses on a gasoline engine.
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