Nice problem, Dave! I assume we're working in general relativity here. No limit (other than C) on speed. Shouldn't we have a limit (20g's, for example) on acceleration? It would appear that standing still while we signal is perhaps the worst thing we can do, so we both want to move as quickly as possible to gain the most time dilation. I would imagine that we both would head for the center of the galaxy, but not too close to the black hole that supposedly lives there. We then both orbit in the plane of the galaxy, one orbiting somewhat faster than the other, so that one will eventually catch up to the other. We both need to realize that the frequence/wavelength of our beacons will be greatly modified by our high speeds & accelerations. Just some thoughts. At 10:35 AM 2/1/2014, Dave Dyer wrote:

You and your buddy have each woken up at some random, unknown point in the milky way galaxy.

You have a very bright, omni-directional beacon that can easily be seen from any point inside it's light cone.

You can travel in any direction, at any speed up to C (but not exceeding it of course).

Your goal is to locate and rendezvous with your buddy for one last drink, sometime before one of you dies of old age.

What's your strategy.