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Computer Science > Data Structures and Algorithms

arXiv:2407.10316v2 (cs)
[Submitted on 14 Jul 2024 (v1), last revised 16 Oct 2025 (this version, v2)]

Title:Online Matroid Embeddings

Authors:Andrés Cristi, Paul Dütting, Robert Kleinberg, Renato Paes Leme, Neel Patel
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Abstract:We introduce the notion of an online matroid embedding, which is an algorithm for mapping an unknown matroid that is revealed in an online fashion to a larger-but-known matroid. We establish the existence of such an embedding for binary matroids, and use it to relate variants of the binary matroid secretary problem to each other, showing that seemingly simpler problems are in fact equivalent to seemingly harder ones (up to constant-factors). Specifically, we show this to be the case for the version of the matroid secretary problem in which the matroid is not known in advance, and where it is known in advance. We also show that the version with known matroid structure, is equivalent to the problem where weights are not fully adversarial but drawn from a known pairwise-independent distribution.
Comments: 45 pages, 5 figures
Subjects: Data Structures and Algorithms (cs.DS); Computer Science and Game Theory (cs.GT)
Cite as: arXiv:2407.10316 [cs.DS]
  (or arXiv:2407.10316v2 [cs.DS] for this version)
  https://doi.org/10.48550/arXiv.2407.10316

Submission history

From: Andrés Cristi [view email]
[v1] Sun, 14 Jul 2024 20:23:15 UTC (37 KB)
[v2] Thu, 16 Oct 2025 20:35:39 UTC (70 KB)
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