English

An algorithm for the weighted metric dimension of two-dimensional grids

Data Structures and Algorithms 2016-02-19 v1 Combinatorics

Abstract

A two-dimensional grid consists of vertices of the form (i,j) for 1 \leq i \leq m and 1 \leq j \leq n, for fixed m,n > 1. Two vertices are adjacent if the \ell_1 distance between their vectors is equal to 1. A landmark set is a subset of vertices L \subseteq V, such that for any distinct pair of vertices u,v \in V, there exists a vertex of L whose distances to u and v are not equal. We design an efficient algorithm for finding a minimum landmark set with respect to total cost in a grid graph with non-negative costs defined on the vertices.

Keywords

Cite

@article{arxiv.1602.05899,
  title  = {An algorithm for the weighted metric dimension of two-dimensional grids},
  author = {Ron Adar and Leah Epstein},
  journal= {arXiv preprint arXiv:1602.05899},
  year   = {2016}
}
R2 v1 2026-06-22T12:53:14.182Z