Professor LaPaugh has worked extensively in the development of algorithms for problems in digital design. She has developed algorithms that use these interactions to find better placements for circuit components. An important application of the work is in the placement of hierarchically defined layouts.

Another focus of Professor LaPaugh's research has been in the synthesis and verification of digital systems from high-level descriptions. Professor LaPaugh has explored the relationship between techniques used by hardware synthesis and program compilation. Many issues are shared by compiler writers for multi-issue machines and synthesis tool writers for special-purpose hardware.

Much of Professor LaPaugh's work is based on the principles of combinatorial algorithm design. In addition to her work in application areas, she has developed and analyzed algorithms for theoretical combinatorial problems such as graph structure problems.