Optimal Error-detection system for Identifying Codes
Assume that a graph $G$ models a detection system for a facility with a possible ``intruder," or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing detectors at a subset of vertices in $G$ to determine the location of an intruder if there is an...
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| Main Authors | , |
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| Format | Journal Article |
| Language | English |
| Published |
11.08.2022
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| Subjects | |
| Online Access | Get full text |
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| Summary: | Assume that a graph $G$ models a detection system for a facility with a
possible ``intruder," or a multiprocessor network with a possible
malfunctioning processor. We consider the problem of placing detectors at a
subset of vertices in $G$ to determine the location of an intruder if there is
any. Many types of detection systems have been defined for different sensor
capabilities; in particular, we focus on Identifying Codes, where each detector
can determine whether there is an intruder within its closed neighborhood. In
this research we explore a fault-tolerant variant of identifying codes
applicable to real-world systems. Specifically, error-detecting identifying
codes permit a false negative transmission from any single detector. We
investigate minimum-sized error-detecting identifying codes in several classes
of graphs, including cubic graphs and infinite grids, and show that the problem
of determining said minimum size in arbitrary graphs is NP-complete. |
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| DOI: | 10.48550/arxiv.2208.06052 |