In one embodiment of the present invention, a support structure generator creates support structures designed to buttress three-dimensional (3D) digital models during 3D printing. In operation, the support structure generator incrementally constructs a support graph that connects overhanging points included in the 3D model with support points on a horizontal ground plane or relatively flat surfaces in the 3D model. After generating the 3D model, the support structure generator translates the connections between the nodes into support posts sized to sufficiently support the connected surfaces with the minimum amount of support material. Advantageously, the support structure is noticeably sparser than conventional support structures that fill a given support region with a solid volume of support material. Consequently, the time necessary for 3D printers to fabricate the support structure of interconnected support posts is less than the time required for 3D printers to fabricate conventional support structures.