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Many  technologically and societally important mathematical problems are intractable for conventional, serial computers. Therefore, a significant need exists for parallel-computing approaches that are capable of solving such problems within reasonable time frames. Recently, we demonstrated a proof-of-principle for a parallel-computation system in which a given combinatorial problem is encoded into a graphical, modular network that is embedded in a nanofabricated planar device. The problem is then solved by a large number of independent biological agents, namely molecular-motor-propelled protein filaments, exploring the network in a highly parallel fashion. Notably, this approach uses orders of magnitude less energy than conventional computers, thus addressing issues related to power-consumption and heat-dissipation.