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In a self-organizing particle system, an abstraction of programmable matter,simple computational elements called particles with limited memory andcommunication self-organize to solve system-wide problems of movement,coordination, and configuration. In this paper, we consider a stochastic,distributed, local, asynchronous algorithm for "shortcut bridging", in whichparticles self-assemble bridges over gaps that simultaneously balanceminimizing the length and cost of the bridge. Army ants of the genus Ecitonhave been observed exhibiting a similar behavior in their foraging trails,dynamically adjusting their bridges to satisfy an efficiency trade-off usinglocal interactions. Using techniques from Markov chain analysis, we rigorouslyanalyze our algorithm, show it achieves a near-optimal balance between thecompeting factors of path length and bridge cost, and prove that it exhibits adependence on the angle of the gap being "shortcut" similar to that of the antbridges. We also present simulation results that qualitatively compare ouralgorithm with the army ant bridging behavior. Our work gives a plausibleexplanation of how convergence to globally optimal configurations can beachieved via local interactions by simple organisms (e.g., ants) with somelimited computational power and access to random bits. The proposed algorithmalso demonstrates the robustness of the stochastic approach to algorithms forprogrammable matter, as it is a surprisingly simple extension of our previousstochastic algorithm for compression.

A Stochastic Approach to Shortcut Bridging in Programmable Matter