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Non-adaptive prophet inequalities for minor-closed classes of matroids.

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Title: Non-adaptive prophet inequalities for minor-closed classes of matroids.
Authors: Pashkovich, Kanstantsin1 (AUTHOR) kpashkov@uwaterloo.ca, Sayutina, Alice1 (AUTHOR) cdkrot0@gmail.com
Source: Discrete Applied Mathematics. Apr2026, Vol. 383, p26-43. 18p.
Subjects: Matroids, Hypothesis, Mathematical analysis
Abstract: We consider the matroid prophet inequality problem. This problem has been extensively studied in the case of adaptive mechanisms. In particular, there is a tight 2-competitive mechanism for all matroids (Kleinberg and Weinberg, 2012). However, it is not known what classes of matroids admit non-adaptive mechanisms with constant guarantee. Recently, in Chawla et al. (2024) it was shown that there are constant-competitive non-adaptive mechanisms for graphic matroids. In this work, we show that various known classes of matroids admit constant-competitive non-adaptive mechanisms. • We show that there exists a 16 -competitive non-adaptive mechanism for graphic matroids in the case of simple graphs. • We show that there exists a (2 k + 2 k) -competitive non-adaptive mechanism for k -column sparse matroids. • We show that there exists a 6 -competitive non-adaptive mechanism for cographic matroids. • We show that there exists a 256 -competitive non-adaptive mechanism for regular matroids. • We show that subject to a Structural Hypothesis, for every prime number p there exists a constant-competitive mechanism for every proper minor-closed class of matroids representable over F p. [ABSTRACT FROM AUTHOR]
Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Non-adaptive prophet inequalities for minor-closed classes of matroids.
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  Data: <searchLink fieldCode="JN" term="%22Discrete+Applied+Mathematics%22">Discrete Applied Mathematics</searchLink>. Apr2026, Vol. 383, p26-43. 18p.
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  Data: We consider the matroid prophet inequality problem. This problem has been extensively studied in the case of adaptive mechanisms. In particular, there is a tight 2-competitive mechanism for all matroids (Kleinberg and Weinberg, 2012). However, it is not known what classes of matroids admit non-adaptive mechanisms with constant guarantee. Recently, in Chawla et al. (2024) it was shown that there are constant-competitive non-adaptive mechanisms for graphic matroids. In this work, we show that various known classes of matroids admit constant-competitive non-adaptive mechanisms. • We show that there exists a 16 -competitive non-adaptive mechanism for graphic matroids in the case of simple graphs. • We show that there exists a (2 k + 2 k) -competitive non-adaptive mechanism for k -column sparse matroids. • We show that there exists a 6 -competitive non-adaptive mechanism for cographic matroids. • We show that there exists a 256 -competitive non-adaptive mechanism for regular matroids. • We show that subject to a Structural Hypothesis, for every prime number p there exists a constant-competitive mechanism for every proper minor-closed class of matroids representable over F p. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.dam.2025.12.001
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      – Code: eng
        Text: English
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        PageCount: 18
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    Subjects:
      – SubjectFull: Matroids
        Type: general
      – SubjectFull: Hypothesis
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      – SubjectFull: Mathematical analysis
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      – TitleFull: Non-adaptive prophet inequalities for minor-closed classes of matroids.
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              Text: Apr2026
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              Y: 2026
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