Let me take a leap of faith here... If I understand your question correctly, you want to draw a map of network nodes or a similar tree-like structure.

Calculating the optimal sector width for each child node is probably just a matter of guessing and adjusting until an acceptable solution is found. You may also want to play a little with other map-drawing software (I use Nagios and yED a lot) to see if any good ideas pop up.

Just don't expect one generic algorithm to be perfectly for all data sets, I doubt that's even possible.