Level Comparison

The below charts show the load balance between the different levels of the tree.

Some observations:

• The cost of rebalancing the first level is the most erratic. I like to think of the algorithm as a sponge and the problem as water seeping through it. First you you have coarse filtering, then it gets more precise.
• The load goes from the top levels to the bottom levels as the bots spread out more.
• The load on the first few levels is not high unless the bots are clumped up.