Question: I came across a couple of similar problems where there are a couple of items in the set **ei = {wi,hi}** for `i=0..n`, you have to find the longest series such that **wm > wm+1** and **hm > hm+1** for each succesive value of `m`.
Does it sound familiar?
Can anyone point out a specific algorithm that may have dealt with similar problems?

Answer: 
One way to do it is to build a directed acyclic graph that has a node for each ei and an edge from ei to ej iff ej > ei (in the sense you state above). Then [find the longest path in this DAG](http://en.wikipedia.org/wiki/Longest_path_problem#Weighted_directed_acyclic_graphs).
You're looking for the longest increasing subsequence, so [patience sorting](http://en.wikipedia.org/wiki/Patience_sorting) is probably the way to go.

When you implement this, you'll need to write your own Comparator method that says `e_i < e_j` if and only if `w_i < w_j` and `h_i < h_j`. The fact that you have a partial order instead of a total order does not change the algorithm.