|   | 
Details
   web
Record
Author Bitar, N.; Goles, E.; Montealegre, P.
Title COMPUTATIONAL COMPLEXITY OF BIASED DIFFUSION-LIMITED AGGREGATION Type
Year 2022 Publication Siam Journal On Discrete Mathematics Abbreviated Journal SIAM Discret. Math.
Volume 36 Issue 1 Pages 823-866
Keywords diffusion-limited aggregation; computational complexity; space complexity; NL-completeness; P-completeness
Abstract 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.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0895-4801 ISBN Medium
Area Expedition Conference
Notes WOS:000778502000037 Approved
Call Number UAI @ alexi.delcanto @ Serial (down) 1558
Permanent link to this record