How to compute the absolute minimum amount of changes to convert one sortorder into another?

Question

Goal

How to encode the data that describes how to re-order a static list from a one order to another order using the minimum amount of data possible?

Answer 1

If you are truly trying to minimize every bit of data going over the wire, how are you transmitting your data? For example, are you compressing it somehow? Using a 32 bit number for sort order is probably overkill if you only have a few thousand items. 16 bits gets you 65000 items for half the $$$. Same goes for the unique ID's.