Either way, here are a few options in handing the situation:
1. Complete Avoidance
If this is a fleeting moment of quick passerby, and you really don't feel comfortable facing the other person, your best bet is to completely avoid them. They might not even notice or see you. Or if they do see you, hopefully they will play the same exact card pretending they didn't see you either. Hide from them if you have to and then get the hell out of there. If they see you, pretend you didn't see them. If you accidentally make eye contact, quickly look away...and then MOVE MOVE MOVE your ass as far away from them as possible. Leave!
2. Quick Subtle Acknowledgement
This is a smile, a wave or a nod. Very brief eye contact and then look away. This is very risky if you don't want to get in a conversation with them. They could perceive this as an invitation to engage in a conversation and "catch up"...uh oh.. if your intention was to avoid a conversation with them, then you need to quickly think of an exit strategy. You won't have that much time as they begin their approach. If you have kids, you need to "pick them up." If you have nieces or nephews you also have to "go pick them up." Or you could be running late to a meeting.. business meeting. Perhaps you need to "go to work"... oh and key phrase "Hi, good to see you.. I gotta run I'm late, but it's great seeing you..OK.take care" ..and once again. MOVE it!
3. Friendly Conversation - Be Oh-SOOO nice.
Sometimes you need to be the better person. By being the better person you are either going to make them feel really good or really guilty. You see them and you give them the biggest smile in the world. Even if you think they are not your friend, you pretend they are and try to be as genuine as you possibly can. If you don't like the person, just remember this: keep your friends close but keep your enemies closer. They don't need to know you don't like them. Say hello. Ask them how they're doing. Try to keep the conversation focused on them and not your life. If they ask about your life, try to keep your answers brief and then go back to suggestion of getting the hello outta there. That's when you excuse yourself and say you "gotta run" but of course make sure you tell them it's good to see them and all that other BS. If they ever did anything mean to you, they will feel bad.
4. Screaming Match/Attack
This is only for those that have replayed your last conversation with this person in your head SO many times and wish you had said something that you didn't say. Or if you left feeling like it would be bad if the two of you ever met in a back alley. It could be your only chance to finally tell them off. When you see them, you approach them with all the anger that you have been holding onto and finally give it to them. Hulk MAD. Hulk SMASH.. Right? No. This won't make things better. This will only make things worse. Don't do it. But if you're gonna do it be ready for things to escalate and be ready to deal with assault and harassment charges.
5. Let It Go and Be Friends Again?
Sometimes, friendships can be salvaged. Not always. But sometimes they can. Maybe enough time has passed. Maybe you have matured or the other person has matured. Maybe you both have matured and you come to the realization that it's silly to hold grudges. You may have had some good reasons for cutting this person out of your life. You don't have to be BFFs, but you can still be on friendly terms