Linking pieces of design information for inspiration are an important part of the early phase of the design process. One key linking operation is assembling, wherein designers create new ideas by assembling partial or whole pieces of ideas together. How designers assemble the ideas reflect their design process. Hence, by developing a computational tool for assembling ideas, the underlying rules of design decision-making might be revealed. In this research, we employed a computational design method consisting of methodological mapping (jigsaw) and consequential analysis (Design Jigsaw system prototype) to create associations between varied types of information at different levels in the design information hierarchy. We then propose a system prototype called Design Jigsaw, based on the analysis of five representation schemes with network-like structures and sound delegation mechanisms. We also developed and explored the representation, components, and the control mechanisms involved in these components. The algorithm of the two main control strategies, grouping and matching/combining, is described in detail along with the procedural description of a jigsaw solving session. Furthermore, we conducted a design experiment to reify the process of the Design Jigsaw system prototype.