## Real Life Search Trees

2007-10-21

I've known this for a while, but was reminded of it when I visited the library today and thought I should share.

The main Northwestern University library has a very strange structure. Inside each level in each tower, the book shelves are arranged in a circle, so that each shelve is on a diameter. Books are arranged by call number along the radius. That is, if you call the direction of the door 0 degrees, the further you go clockwise, the higher the call number.

To make the NU library configuration clearer, here's a map of a standard floor. The lines arranged in a circle are shelves.

Compared to normal libraries, where the shelves are arranged by call number in rows, this makes no sense at all. But get this: finding a call number is quicker in the circular system than the traditional system.

Here's the reason. Because the shelves at NU are not all along the circumference, but have a distance from the center, the shelves essentially form a search tree. Instead of starting from where you enter, you walk to the center first. Then just follow down the aisle which has a call number closest to the book you want. In mathematical terms, the shelves have a depth of roughly 3 and a branching factor of 2, which makes the books really easy to find. Of course, once you get to the correct shelf you have to find the book the normal way.

In contrast to the tree structure of NU library, traditional libraries is a linked list. You have to walk through shelves with a lower number before you get to the shelf you want. There's no short cut for this process. Therefore, the NU library search time is logarithmic (log base 2), while traditional libraries have a linear search time.

I don't think too many people know this. Today was the first time I saw someone (besides myself) going to the center first and finding books that way. Shame.