Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Fault-Tolerant Detection Systems on the King's Grid

Version 1 : Received: 16 January 2022 / Approved: 18 January 2022 / Online: 18 January 2022 (09:43:55 CET)

How to cite: Jean, D.; Seo, S. Fault-Tolerant Detection Systems on the King's Grid. Preprints 2022, 2022010249 (doi: 10.20944/preprints202201.0249.v1). Jean, D.; Seo, S. Fault-Tolerant Detection Systems on the King's Grid. Preprints 2022, 2022010249 (doi: 10.20944/preprints202201.0249.v1).

Abstract

A detection system, modeled in a graph, uses "detectors" on a subset of vertices to uniquely identify an "intruder" at any vertex. We consider two types of detection systems: open-locating-dominating (OLD) sets and identifying codes (ICs). An OLD set gives each vertex a unique, non-empty open neighborhood of detectors, while an IC provides a unique, non-empty closed neighborhood of detectors. We explore their fault-tolerant variants: redundant OLD (RED:OLD) sets and redundant ICs (RED:ICs), which ensure that removing/disabling at most one detector guarantees the properties of OLD sets and ICs, respectively. This paper focuses on constructing optimal RED:OLD sets and RED:ICs on the infinite king's grid, and presents the proof for the bounds on their minimum densities; [3/10, 1/3] for RED:OLD sets and [3/11, 1/3] for RED:ICs.

Keywords

domination, detection system, identifying-code, open-locating-dominating set, fault-tolerant, king's grid, density

Subject

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 0
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.