nested boxes algorithm I am given a set of 3D boxes {$B_1$, $B_2$...$B_n$} and each box have length, width and height. But these values are interchangeable since I can rotate the box. I need to find out the maximum sequence of nested boxes.

I have tried this problem using sort. But I still get stuck. I used built in sort function to sort all boxes by length in ascending order. I read the reference about this question and learned that people used radix sort. I have know idea how radix sort is applied here because all sorts I am familiar is comparison sort.
One solution that comes to mind is to first build a directed graph where every vertex represents a vertex. An edge goes from Box A to Box B if B fits into A. One can easily verify that this graph contains no cycles. A maximum sequence of nested boxes is equivalent to the longest path in this directed acyclic graph. A longest path in a DAG can be found by using a topological sort on the graph. 

This surely is a bit overkill and is probably also not the most efficient solution ($O(n^2)$ for building the graph).