As a generalization, you may find it useful to work with or develop a formal description method for your area, and prove useful transformations and inculcate intuition. I wouldn't claim this as uniquely EDA, however, researchers interested primarily in EDA have made contributions in this area. The logic optimization community is the hotbed of algorithm development based on these data structures. In order to transform parallel behavior into structure, EDA researchers have advanced the field of Data-Flow analysis, generally using Petri nets or Value Trace algorithms. The greed for speed is, if anything, even greater in the EDA community than it is in the general compilation community.
Code generation is a vital issue.
Algorithm analysis and computational complexity. Logic minimization algorithms are generally NP, so a lot of bright people have been studying issues of computational complexity. Linear programming is a general optimization technique I know that some recently patented linear programming algorithms in were developed by boolean logic optimization researchers. The EDA branch most often associated with this kind of algorithm is critical path timing analysis. A lot of work has gone into partitioning.