I have a person like that in my work-a-day life ~ a person for whom I am a constant reminder of something distasteful to her. We do a dance of sorts: I enter the room, she leaves; if I'm in the room already, she does not acknowledge me; when she's in the room, I walk past without saying anything. It's become the 'elephant in the living room' for us. My 'strategy' ~ such as it is ~ is to have as little contact as possible. I have viewed that as the 'safe' approach.
Internally, I've needed to distance myself from the negative energy that snaps between us when we're near each other. Forgiveness and compassion have become my greatest allies. Whenever I catch myself spiraling into the negative chatter inside my head, I remind myself that no one is that negative without being wounded herself. Mostly, this is self-talk about the stress she is or must be under, any good/talented actions I've observed her doing, examining how I have fit or fed into her negative space. This exercise works to keep me both humbled and focused on the other person; both of these keep positive energy in view.
What are your strategies?