Tolerance to Asynchrony of an Algorithm for Gathering Myopic Robots on an Infinite Triangular Grid
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914637133381632 |
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| author | Gupta, Arya Tanmay Kulkarni, Sandeep S |
| author_facet | Gupta, Arya Tanmay Kulkarni, Sandeep S |
| contents | In this paper, we study the problem of gathering distance-1 myopic robots on an infinite triangular grid. We show that the algorithm developed by Goswami et al. (SSS, 2022) is lattice-linear (cf. Gupta and Kulkarni, SRDS 2023). This implies that a distributed scheduler, assumed therein, is not required for this algorithm: it runs correctly in asynchrony. It also implies that the algorithm works correctly even if the robots are equipped with a unidirectional \textit{camera} to see the neighbouring robots (rather than an omnidirectional one, which would be required under a distributed scheduler). Due to lattice-linearity, we can predetermine the point of gathering. We also show that this algorithm converges in $2n$ rounds, which is lower than the complexity ($2.5(n+1)$ rounds) that was shown in Goswami et al. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_13080 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tolerance to Asynchrony of an Algorithm for Gathering Myopic Robots on an Infinite Triangular Grid Gupta, Arya Tanmay Kulkarni, Sandeep S Distributed, Parallel, and Cluster Computing In this paper, we study the problem of gathering distance-1 myopic robots on an infinite triangular grid. We show that the algorithm developed by Goswami et al. (SSS, 2022) is lattice-linear (cf. Gupta and Kulkarni, SRDS 2023). This implies that a distributed scheduler, assumed therein, is not required for this algorithm: it runs correctly in asynchrony. It also implies that the algorithm works correctly even if the robots are equipped with a unidirectional \textit{camera} to see the neighbouring robots (rather than an omnidirectional one, which would be required under a distributed scheduler). Due to lattice-linearity, we can predetermine the point of gathering. We also show that this algorithm converges in $2n$ rounds, which is lower than the complexity ($2.5(n+1)$ rounds) that was shown in Goswami et al. |
| title | Tolerance to Asynchrony of an Algorithm for Gathering Myopic Robots on an Infinite Triangular Grid |
| topic | Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2307.13080 |