Furniture typically consists of assemblies of elongated and planar parts that are connected together by glue, nails, hinges, screws, or other means that do not encourage disassembly and re-assembly. An alternative approach is to use an interlocking mechanism, where the component parts tightly interlock with one another. The challenge in designing such a network of interlocking joints is that local analysis is insufficient to guarantee global interlocking, and there is a huge number of joint combinations that require an enormous exploration effort to ensure global interlocking. In this paper, we present a computational solution to support the design of a network of interlocking joints that form a globally-interlocking furniture assembly. The key idea is to break the furniture complex into an overlapping set of small groups, where the parts in each group are immobilized by a local key, and adjacent groups are further locked with dependencies. The dependency among the groups saves the effort of exploring the immobilization of every subset of parts in the assembly, thus allowing the intensive interlocking computation to be localized within each small group. We demonstrate the effectiveness of our technique on many globally-interlocking furniture assemblies of various shapes and complexity.