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Decentralized Dynamic Stable Matching — arXiv:2610.41912

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.41912
License (as archived): CC0-1.0
Archived: 2026-11-02T07:45:27.198Z
SHA-256 of the archived text: cc16c8aff3e2c809d2dac6ec2259f2584e952fc8e544c078c85ed2d2fbe49293
Stable URL of this page: https://metraipolis.com/documento/dc_a8bfcefcb467

How to cite

Decentralized Dynamic Stable Matching — arXiv:2610.41912 — arXiv (en), https://arxiv.org/abs/2610.41912 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_a8bfcefcb467 (Metraipolis archive dc_a8bfcefcb467, sha256 cc16c8aff3e2c809d2dac6ec2259f2584e952fc8e544c078c85ed2d2fbe49293)

BibTeX

@misc{dca8bfcefcb467,
  title = {Decentralized Dynamic Stable Matching — arXiv:2610.41912},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.41912},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_a8bfcefcb467; sha256 cc16c8aff3e2c809d2dac6ec2259f2584e952fc8e544c078c85ed2d2fbe49293},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.41912. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study decentralized computation of the player-optimal stable matching (POSM) with unannounced player arrivals and departures. Without a common clock, event information, or direct communication, players propose to arms and observe only their own accept/reject outcomes. Mismatch cost counts rounds when the realized matching differs from the current POSM. For known preferences, we give a deterministic polynomial-time self-calibrating protocol with cost $O(t_*+K^2\log T)$, improving the previous bound $O(T^{1-1/K}(\log T)^{2/K})$. Here $K$ is the number of arms, $t_*$ the last event time, and $T$ the horizon. Players use only local time and proposal outcomes, knowing neither $t_*$ nor $T$. For any nondecreasing, polynomial-time-computable $g(t)=\Omega(t)$, the protocol achieves $O(g(t_*)+K^2N_g(T))$. Here $g$ governs recovery time, while $N_g(T)$ counts iterations of $t\mapsto t+g(t)$ below $T$, exposing a tradeoff between recovery time and asymptotic mismatch cost. Any randomized protocol with recovery scale $g(t)\ge1$ and sublinear asymptotic mismatch cost has worst-case expected cost $\Omega(t_*+N_g(T))$. Thus, with $g(t)=t$, our protocol is optimal up to a $K^2$ factor among sublinear-cost protocols with $O(t_*)$ recovery time. For unknown preferences on both sides, each player and arm learns its preferences from its own observations after matching. We give a decentralized learning protocol with expected cost $O(t_*+K^4\Delta_{\mathrm{min}}^{-2}\log T)$, where $\Delta_{\mathrm{min}}$ measures preference gaps. A complementary static-setting lower bound adapted from the literature shows that the dependence on $T$ and $\Delta_{\mathrm{min}}$ is tight.

Tema degli esploratori: calcolo e infrastrutture (elenco arXiv cs.DC, nuovi lavori del giorno).
Categorie arXiv: Distributed, Parallel, and Cluster Computing (cs.DC).
Pagina del lavoro: https://arxiv.org/abs/2610.41912 — 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 2026-11-02T07:37:30.167Z dalla pagina https://arxiv.org/list/cs.DC/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).