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Hardness of Approximation of Rank Aggregation on Ulam Metric — arXiv:2608.29180

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.29180
License (as archived): CC0-1.0
Archived: 2026-10-17T10:07:18.030Z
SHA-256 of the archived text: 5b91500bce302b72634cfb526d220ffd4e8521c1b360d6ae7f261a1490dbc7cc
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How to cite

Hardness of Approximation of Rank Aggregation on Ulam Metric — arXiv:2608.29180 — arXiv (en), https://arxiv.org/abs/2608.29180 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_71b5f75fa784 (Metraipolis archive dc_71b5f75fa784, sha256 5b91500bce302b72634cfb526d220ffd4e8521c1b360d6ae7f261a1490dbc7cc)

BibTeX

@misc{dc71b5f75fa784,
  title = {Hardness of Approximation of Rank Aggregation on Ulam Metric — arXiv:2608.29180},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.29180},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_71b5f75fa784; sha256 5b91500bce302b72634cfb526d220ffd4e8521c1b360d6ae7f261a1490dbc7cc},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.29180. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study the approximability of rank aggregation under the Ulam metric. In the \emph{Ulam median} problem, the goal is to find a permutation minimizing the sum of its Ulam distances to the input permutations, while in the \emph{Ulam center} problem the objective is to minimize the maximum such distance. Both problems are known to be NP-hard, but no explicit approximation hardness was previously known. We prove that, for every $\varepsilon>0$, it is NP-hard to approximate either Ulam median or Ulam center within a factor of $51/50-\varepsilon$, even when the input consists of only four permutations. We further show that unless P = NP, neither problem admits a polynomial-time additive approximation scheme. The hardness result for Ulam median is established via a reduction from MAX-E3-LIN-2. The corresponding hardness for Ulam center is then obtained through a reduction from Ulam median.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-01 in cs.DS).
Categorie arXiv: Computational Complexity (cs.CC) ; Data Structures and Algorithms (cs.DS).
Pagina del lavoro: https://arxiv.org/abs/2608.29180 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T10:00:01.297Z dalla pagina https://arxiv.org/catchup/cs.DS/2026-09-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).