An alignment problem
Data Structures and Algorithms
2024-11-14 v1 Computational Complexity
Abstract
This work concerns an alignment problem that has applications in many geospatial problems such as resource allocation and building reliable disease maps. Here, we introduce the problem of optimally aligning collections of spatial supports over spatial units in a -dimensional Euclidean space. We show that the 1-dimensional case is solvable in time polynomial in , and . We then show that the 2-dimensional case is NP-hard for 2 collections of 2 supports. Finally, we devise a heuristic for aligning a set of collections in the 2-dimensional case.
Cite
@article{arxiv.2411.08792,
title = {An alignment problem},
author = {Emma L. McDaniel and Armin R. Mikler and Chetan Tiwari and Murray Patterson},
journal= {arXiv preprint arXiv:2411.08792},
year = {2024}
}