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Online Matroid Embeddings

Authors Andrés Cristi , Paul Dütting , Robert Kleinberg , Renato Paes Leme , Neel Patel

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Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Theory of computation → Random projections and metric embeddings
Keywords
  • Matroids
  • Secretary Problem
  • Online Algorithm

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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. The existence of such embedding enables a reduction from the version of the matroid secretary problem where the matroid is unknown to the version where the matroid is known in advance. 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 binary 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.

Cite As Get BibTex

Andrés Cristi, Paul Dütting, Robert Kleinberg, Renato Paes Leme, and Neel Patel. Online Matroid Embeddings. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 69:1-69:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.69

Author Details

Andrés Cristi
  • EPFL, Lausanne, Switzerland
Paul Dütting
  • Google Research, Zürich, Switzerland
Robert Kleinberg
  • Cornell University, Ithaca, NY, USA
  • Google Research, New York, NY, USA
Renato Paes Leme
  • Google Research, New York, NY, USA
Neel Patel
  • Google Research, Zürich, Switzerland

Funding

  • Cristi, Andrés: Partially funded by the Center for Mathematical Modeling (CMM), FB210005, BASAL funds for centers of excellence (ANID-Chile).

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