I would say two things
1) An apology from the parent (or the child, if appropriate for the age)
2) Evidence that the parent is taking it seriously, and is actively working to solve the problem.
The second part is important, because that's what's going to determine if your kid is welcome to play with the other children, and it will vary depending on the child, their age, and the offense.
If you have a regular playgroup, then you can pre-emptively discuss this with the other parents - explain that your child is currently having trouble with X, and that you're working on it, and ask for their help in patrolling (in case you miss an instance).
For more general groups or at the playground - for something like in the OP, it could mean making sure you're always within arms reach of the child to keep them from hitting the other children. Or it could mean that as soon as they hit a kid, you swoop down with a firm "no hitting - that hurts people", take away the toys, and immediately take your child out of the building and home repeating "you can't play if you hit people" a few times (as time-outs are ineffective). It can also be worth talking to your pediatrician, or a child psychologist, for specific advice.
If you get into a cycle of child hitting another child for no reason, having a time out, going back to play and repeating - after a few rounds of this, the other parents are going to get fed up, and possibly start keeping their kids away from yours.