Divide a star catalogue to optimize star search
This is really a computing problem, but I suppose the only point from an astronomical perspective is what the RA, Dec distributions of your catalogues look like.

I'm not that familiar with optimal search techniques but I guess that you want roughly similar numbers of stars in each region.

If your catalogue is just of the brightest stars, then these are fairly uniformly distributed around the sky, so splitting them up in equal bands of right ascension would probably do.

However, if you are dealing with much larger catalogues then there is likely to be a significant concentration towards the galactic plane. In these circumstance you might be better off splitting your regions in terms of their galactic latitude. So you would calculate galactic coordinates by transforming the RA, Dec and then plot the distribution of number of stars versus galactic latitude to see where you would split your regions.