Have You Ever Played This Game?

I played a great game tonight and I'm sure you've played it too. If you're anything like me when you grocery shop, you use the "start at the first aisle and go up and down each aisle" strategy. While this strategy has a great number of benefits (i.e., cover a lot of ground quickly, able to recognize things you'd otherwise forget, exercise), it does, however, have a few setbacks - namely, running alongside someone else who has the exact same strategy as you.

So, I'm in the grocery store tonight, and I begin at the first aisle. I scurry down the lengthy line of shelving, make a turn to go down to the next aisle, and run into a woman going to the next aisle. I smile half-heartedly and continue about my business. I quickly move into the next aisle, only to be confronted by the same woman. I now have a choice: do I acknowledg her with another smile, ignore her, strike up coversation, say something witty... I don't know. So I opted for the ignorning strategy. I continue onto what becomes a 30 minute game of weaving in and out of aisles and meeting somewhere in the middle with my new friend. It was almost as if we were involved in an intricate dance within the aisles. Sometimes she would lead, other times I would (this of course means that I would arrive in the next aisle before her). It was all the elegance that one such Kroger could handle.

Now here's my question: Is there some sort of social ettiquette that I should have adhered to in this situation?