English

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 kk collections of mm spatial supports over nn spatial units in a dd-dimensional Euclidean space. We show that the 1-dimensional case is solvable in time polynomial in kk, mm and nn. 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.

Keywords

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}
}