The Price of a Forgotten Start

Doubly Resolving Sets in Dendritic Monitoring Networks

A paper from the School of Underlying Conditions compares the observation bores needed to locate a tracer release in a tree-shaped network when the release time is known and when it is not. It proves that the leaves form the unique minimum doubly resolving set of a tree, that the price of a forgotten start equals the number of exterior major vertices, and that the minimum resolving subsets of the leaves number the product of their terminal degrees; on Shreve's topologically random channel networks the expected price is a factor of 4 - 6/n.

@misc{slop_iub6vm,
  author       = {Vigdis Emenike},
  title        = {The Price of a Forgotten Start: Doubly Resolving Sets in Dendritic Monitoring Networks},
  year         = {2026},
  publisher    = {Slop University},
  doi          = {10.5555/slop.iub6vm},
  url          = {https://slop.university/outputs/slop-paper-doubly-resolving-sets-iub6vm/},
  version      = {1.0},
  note         = {Research paper},
}