Randomized $k$-server in polynomial time
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911640547491840 |
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| author | Coester, Christian Cosson, Romain |
| author_facet | Coester, Christian Cosson, Romain |
| contents | We study the design of computationally efficient randomized algorithms for the $k$-server problem. Existing randomized algorithms with the best known competitive ratios are, on the one hand, inherently implicit and, on the other hand, employ a rounding scheme that maintains a distribution over exponentially many configurations. In this work, we introduce a derandomization framework that transforms any randomized $k$-server algorithm on a hierarchically separated tree into one that uses only $O(\log k)$ random bits for request sequences of arbitrary length; hence maintaining a distribution over only polynomially many server configurations. Leveraging this black-box derandomization, we obtain the first polynomial-time randomized $k$-server algorithm on arbitrary $n$-point metrics with a polylogarithmic competitive ratio. Our results also have implications for the advice complexity of the $k$-server problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01497 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Randomized $k$-server in polynomial time Coester, Christian Cosson, Romain Data Structures and Algorithms We study the design of computationally efficient randomized algorithms for the $k$-server problem. Existing randomized algorithms with the best known competitive ratios are, on the one hand, inherently implicit and, on the other hand, employ a rounding scheme that maintains a distribution over exponentially many configurations. In this work, we introduce a derandomization framework that transforms any randomized $k$-server algorithm on a hierarchically separated tree into one that uses only $O(\log k)$ random bits for request sequences of arbitrary length; hence maintaining a distribution over only polynomially many server configurations. Leveraging this black-box derandomization, we obtain the first polynomial-time randomized $k$-server algorithm on arbitrary $n$-point metrics with a polylogarithmic competitive ratio. Our results also have implications for the advice complexity of the $k$-server problem. |
| title | Randomized $k$-server in polynomial time |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2605.01497 |