A Lower Bound on the Competitive Ratio of the Permutation Algorithm for Online Facility Assignment on a Line
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909117989257216 |
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| author | Harada, Tsubasa |
| author_facet | Harada, Tsubasa |
| contents | In the online facility assignment on a line (OFAL) with a set $S$ of $k$ servers and a capacity $c:S\to\mathbb{N}$, each server $s\in S$ with a capacity $c(s)$ is placed on a line and a request arrives on a line one-by-one. The task of an online algorithm is to irrevocably assign a current request to one of the servers with vacancies before the next request arrives. An algorithm can assign up to $c(s)$ requests to each server $s\in S$.
In this paper, we show that the competitive ratio of the permutation algorithm is at least $k+1$ for OFAL where the servers are evenly placed on a line. This disproves the result that the permutation algorithm is $k$-competitive by Ahmed et al.. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12734 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Lower Bound on the Competitive Ratio of the Permutation Algorithm for Online Facility Assignment on a Line Harada, Tsubasa Data Structures and Algorithms Discrete Mathematics In the online facility assignment on a line (OFAL) with a set $S$ of $k$ servers and a capacity $c:S\to\mathbb{N}$, each server $s\in S$ with a capacity $c(s)$ is placed on a line and a request arrives on a line one-by-one. The task of an online algorithm is to irrevocably assign a current request to one of the servers with vacancies before the next request arrives. An algorithm can assign up to $c(s)$ requests to each server $s\in S$. In this paper, we show that the competitive ratio of the permutation algorithm is at least $k+1$ for OFAL where the servers are evenly placed on a line. This disproves the result that the permutation algorithm is $k$-competitive by Ahmed et al.. |
| title | A Lower Bound on the Competitive Ratio of the Permutation Algorithm for Online Facility Assignment on a Line |
| topic | Data Structures and Algorithms Discrete Mathematics |
| url | https://arxiv.org/abs/2402.12734 |