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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2504.14124 |
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| _version_ | 1866908328136802304 |
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| author | Jean, Devin Seo, Suk |
| author_facet | Jean, Devin Seo, Suk |
| contents | The concept of an identifying code for a graph was introduced by Karpovsky, Chakrabarty, and Levitin in 1998 as the problem of covering the vertices of a graph such that we can uniquely identify any vertex in the graph by examining the vertices that cover it. An application of an identifying code would be to detect a faulty processor in a multiprocessor system. In 2020, a variation of identify code called "self-identifying code" was introduced by Junnila and Laihonen, which simplifies the task of locating the malfunctioning processor. In this paper, we continue to explore self-identifying codes. In particular, we prove the problem of determining the minimum cardinality of a self-identifying code for an arbitrary graph is NP-complete and we investigate minimum-sized self-identifying code in several classes of graphs, including cubic graphs and infinite grids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14124 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Progress on Self Identifying Codes Jean, Devin Seo, Suk Discrete Mathematics Combinatorics The concept of an identifying code for a graph was introduced by Karpovsky, Chakrabarty, and Levitin in 1998 as the problem of covering the vertices of a graph such that we can uniquely identify any vertex in the graph by examining the vertices that cover it. An application of an identifying code would be to detect a faulty processor in a multiprocessor system. In 2020, a variation of identify code called "self-identifying code" was introduced by Junnila and Laihonen, which simplifies the task of locating the malfunctioning processor. In this paper, we continue to explore self-identifying codes. In particular, we prove the problem of determining the minimum cardinality of a self-identifying code for an arbitrary graph is NP-complete and we investigate minimum-sized self-identifying code in several classes of graphs, including cubic graphs and infinite grids. |
| title | Progress on Self Identifying Codes |
| topic | Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2504.14124 |