Often it is good to address the need that is stated rather than answering the question that was asked. I would like only to point out that there is a well-known parallel solution that neatly circumvents all the technical computing issues: Santa has helpers. These agents work asynchronously and independently to identify the houses that need visits and carry out the deliveries. No special GIS computation on Santa's part is needed.
It is wonderful that this technology scales, so that as the world's (Christian) population has expanded by several orders of magnitude over the millennia, Santa's ability to carry out his duties has never seriously been in doubt: the number of available helpers has grown in direct proportion to the number of houses that need visits.
There is a physical demonstration of the existence of these helpers. If, to assume the contrary, just one individual tried to deliver gifts to, say, one billion dwellings throughout the course of a calendar day (which spans 48 hours, accounting for time zones), they would have to visit almost 6000 dwellings per second. A lower bound for the mean distance between dwellings is afforded by the density of the world's larger cities, in which people may live only 10 meters or so apart. This would require an average speed of 6000 * 10 = 60,000 meters per second, far surpassing the sound barrier (creating sonic booms that are not heard on Christmas) and creating so much atmospheric friction that the sleigh would become a blazing fireball destroying everything in its proximity. Although this gives us a new understanding of the origin of the red glow in Rudolph's nose, it clearly demonstrates that only a parallel solution is even possible, QED.