High-throughput, data-directed computational protocols for Structural Genomics (or Proteomics) are required in order to evaluate the protein products of genes for structure and function at rates comparable to current gene-sequencing technology. This paper presents the JIGSAW algorithm, a novel high-throughput, automated approach to protein structure characterization with nuclear magnetic resonance (NMR). JIGSAW applies graph algorithms and probabilistic reasoning techniques, enforcing first-principles consistency rules in order to overcome a 5-10% signal-to-noise ratio. It consists of two main components: (1) graph-based secondary structure pattern identification in unassigned heteronuclear NMR data, and (2) assignment of spectral peaks by probabilistic alignment of identified secondary structure elements against the primary sequence. Deferring assignment eliminates the bottleneck faced by traditional approaches, which begin by correlating peaks among dozens of experiments. JIGSAW utilizes only four experiments, none of which requires 13C-labeled protein, thus dramatically reducing both the amount and expense of wet lab molecular biology and the total spectrometer time. Results for three test proteins demonstrate that JIGSAW correctly identifies 79-100% of alpha-helical and 46-65% of beta-sheet NOE connectivities and correctly aligns 33-100% of secondary structure elements. JIGSAW is very fast, running in minutes on a Pentium-class Linux workstation. This approach yields quick and reasonably accurate (as opposed to the traditional slow and extremely accurate) structure calculations. It could be useful for quick structural assays to speed data to the biologist early in an investigation and could in principle be applied in an automation-like fashion to a large fraction of the proteome.