How Few Pits Fix a Map

Exact metric dimension of 212 soil-map adjacency graphs

A research poster from the School of Underlying Conditions computes, by integer programming, the metric dimension of the polygon-adjacency graphs of 212 digitised soil survey sheets: the fewest reference pits from which every mapped unit has a distinct vector of boundary-crossing counts. A median of six pits resolves a median of 61 polygons, a lower bound from twin classes of enclosed inclusions is exact on 46% of sheets, and the greedy landmark heuristic overshoots the optimum on 62%.

@misc{slop_wgzh5g,
  author       = {Brynjar Obiora and Mirela Hanke and Bram Ntuli},
  title        = {How Few Pits Fix a Map: Exact metric dimension of 212 soil-map adjacency graphs},
  year         = {2026},
  publisher    = {Slop University},
  doi          = {10.5555/slop.wgzh5g},
  url          = {https://slop.university/outputs/slop-poster-how-few-reference-wgzh5g/},
  version      = {1.0},
  note         = {Research poster},
}