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Prophet Secretary for k-Knapsack and l-Matroid Intersection via Continuous Exchange Property

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Combinatorial Algorithms (IWOCA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12757))

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Abstract

We study the k-knapsack and l-matroid constrained prophet secretary problem, which is a combinatorial prophet secretary problem whose feasible domain is the intersection of k-knapsack constraints and l-matroid constraints. Here, the prices of the items and the structure of the matroids are deterministic and known in advance, and the values of the items are stochastic and their distributions are known in advance. We derive a constant-factor approximation algorithm for this problem. We adapt Ehsani et al. (2018)’s technique for the matroid constraint to the knapsack constraint via continuous relaxation. For this purpose, we prove an “exchange property” of the knapsack constraint.

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Authors and Affiliations

  1. The University of Tokyo, Tokyo, Japan

    Soh Kumabe

  2. RIKEN, Wako, Japan

    Takanori Maehara

Authors
  1. Soh Kumabe
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  2. Takanori Maehara
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Correspondence to Soh Kumabe .

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Editors and Affiliations

  1. University of Ottawa, Ottawa, ON, Canada

    Paola Flocchini

  2. University of Ottawa, Ottawa, ON, Canada

    Lucia Moura

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Kumabe, S., Maehara, T. (2021). Prophet Secretary for k-Knapsack and l-Matroid Intersection via Continuous Exchange Property. In: Flocchini, P., Moura, L. (eds) Combinatorial Algorithms. IWOCA 2021. Lecture Notes in Computer Science(), vol 12757. Springer, Cham. https://doi.org/10.1007/978-3-030-79987-8_30

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  • DOI: https://doi.org/10.1007/978-3-030-79987-8_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-79986-1

  • Online ISBN: 978-3-030-79987-8

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