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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]
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Database: Engineering Source
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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]
ISSN:0166218X
DOI:10.1016/j.dam.2025.12.001