COMPUTATIONAL COMPLEXITY OF BIASED DIFFUSION-LIMITED AGGREGATION
Bitar
N
author
Goles
E
author
Montealegre
P
author
2022
Diffusion-Limited Aggregation (DLA) is a cluster-growth model that consists in a set of particles that are sequentially aggregated over a two-dimensional grid. In this paper, we introduce a biased version of the DLA model, in which particles are limited to move in a subset of possible directions. We denote by k-DLA the model where the particles move only in k possible directions. We study the biased DLA model from the perspective of Computational Complexity, defining two decision problems The first problem is Prediction, whose input is a site of the grid c and a sequence S of walks, representing the trajectories of a set of particles. The question is whether a particle stops at site c when sequence S is realized. The second problem is Realization, where the input is a set of positions of the grid, P. The question is whether there exists a sequence S that realizes P, i.e. all particles of S exactly occupy the positions in P. Our aim is to classify the Prediciton and Realization problems for the different versions of DLA. We first show that Prediction is P-Complete for 2-DLA (thus for 3-DLA). Later, we show that Prediction can be solved much more efficiently for 1-DLA. In fact, we show that in that case the problem is NL-Complete. With respect to Realization, we show that restricted to 2-DLA the problem is in P, while in the 1-DLA case, the problem is in L.
diffusion-limited aggregation
computational complexity
space complexity
NL-completeness
P-completeness
WOS:000778502000037
exported from refbase (show.php?record=1558), last updated on Thu, 21 Apr 2022 12:37:39 -0400
text
10.1137/18M1215815
Bitar_etal2022
Siam Journal On Discrete Mathematics
SIAM Discret. Math.
2022
continuing
periodical
academic journal
36
1
823
866
0895-4801