The k-server conjecture is true
Researchers Christian Coester, Elias Koutsoupias, and Marek Zbysiński have proven the k-server conjecture, a long-standing problem in computer science. The proof demonstrates that the work function algorithm achieves a competitive ratio of k on every metric space. The mathematical approach utilizes a matrix-based algebraic representation of the work function to facilitate the amortized analysis.
- ▪The k-server conjecture states that a deterministic online algorithm can achieve a competitive ratio of k on every metric space.
- ▪The authors prove that the work function algorithm satisfies this conjecture.
- ▪The proof employs a natural algebraic representation of the work function as a matrix that encodes feasible paths to configurations.
- ▪In this representation, work function values correspond to the determinant of k columns of the matrix.
- ▪The amortized analysis relies on a potential function defined using a larger matrix derived from the original representation.
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| Original publisher | arXiv.org |
| Canonical URL | https://arxiv.org/abs/2609.15979 |
| Publication time | Tue, 15 Sep 2026 07:45:31 +0000 |
| Retrieval time | 2026-09-15T10:16:53.615Z |
| Last seen | 2026-09-15T10:16:53.615Z |
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| Summary source text | contentText |
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| Cluster | WdVhLLb9qzi4 · 1 stories |
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| Commercial reuse | May the content be reused commercially? | Not permitted |
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Computer Science > Data Structures and Algorithms arXiv:2609.15979 (cs) [Submitted on 14 Sep 2026] Title:The $k$-server conjecture is true Authors:Christian Coester, Elias Koutsoupias, Marek Zbysiński View a PDF of the paper titled The $k$-server conjecture is true, by Christian Coester and 2 other authors View PDF HTML (experimental) Abstract:The $k$-server conjecture states that a deterministic online algorithm can achieve competitive ratio $k$ on every metric space. We prove the conjecture. Specifically, we show that the work function algorithm satisfies it. Our proof uses a natural algebraic representation of the work function as a matrix, which encodes all feasible paths to reach a configuration.
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