1. I'm not sure. It's only my assumption, but it should definitely be verified. Obviously if the assumption is bad then my conclusion is no good.
2. Several broad categories of solutions spring to mind with their own tradeoffs:
2.1 Invest in rehabilitation. Difficulties are cost and probably political problems due to ignorance (or maybe I'm ignorant for my faith in rehabilitation?).
2.2 Longer sentencing (or rather require prisoners to serve more of their sentence more frequently, as opposed to early probation, etc). Downside is cost, ethics, and politics (a lot of well-meaning, typically upper- and upper-middle-class folks believe that longer sentences harms communities of color more than violent re-offenders, or rather they don't consider the costs of the latter).
2.3 Death penalty. Downside is ethics.