Computational Complexity of Biased Diffusion-Limited Aggregation

Diffusion-limited aggregation (DLA) is a cluster-growth model that consists of set particles are sequentially aggregated over two-dimensional grid. In this paper, we introduce biased version the DLA model, in which limited to moving subset possible directions. We denote by $k$-DLA where move only $k$ study from perspective computational complexity, defining two decision problems. The first problem Prediction, whose input site grid $c$ and sequence $S$ walks, representing trajectories particles. question whether particle stops at when realized. second Realization, positions grid, $P$. there exists realizes $P$, i.e., all exactly occupy Our aim classify Prediction Realization problems for different versions DLA. show P-Complete 2-DLA (thus 3-DLA). Later, can be solved much more efficiently 1-DLA. fact, case, NL-Complete. With respect restricted P, while 1-DLA L.