Some sort of restitution and restoration process is of course needed as well.
Well, of course, you only ostracize if restitution is refused.
I still have yet to be given a compelling argument for how ostracizing murderers keeps them from murdering again.
The idea is that you remove the social support structure, preventing the criminal from doing anything in the society, until restitution is paid. It does not keep them from murdering again, the idea is that it will enforce the repayment of his/her debt in the least inhumane way possible. What keeps them from murdering again is the fact that it's an armed society, and he's less likely to survive with each attempted murder.
That said, I support rehabilitation/restitution for lesser crimes, but premeditated murder, there is no way to repay. Let the family and friends of the victim decide what will best repay that debt.