Direct projection of 3D branching structures, such as networks of cables, blood vessels, or neurons onto a 2D image creates the illusion of intersecting structural parts and creates challenges for understanding and communication. We present a method for visualizing such structures, and demonstrate its utility in visualizing the abdominal aorta and its branches, whose tomographic images might be obtained by computed tomography or magnetic resonance angiography, in a single 2D stylistic image, without overlaps among branches. The visualization method, termed uncluttered single-image visualization (USIV), involves optimization of geometry. This paper proposes a novel optimization technique that utilizes an interesting connection of the optimization problem regarding USIV to the protein structure prediction problem. Adopting the integer linear programming-based formulation for the protein structure prediction problem, we tested the proposed technique using 30 visualizations produced from five patient scans with representative anatomical variants in the abdominal aortic vessel tree. The novel technique can exploit commodity-level parallelism, enabling use of general-purpose graphics processing unit (GPGPU) technology that yields a significant speedup. Comparison of the results with the other optimization technique previously reported elsewhere suggests that, in most aspects, the quality of the visualization is comparable to that of the previous one, with a significant gain in the computation time of the algorithm.