Strong Algorithms for the Ordinal Matroid Secretary Problem

Soto, José A.; Turkieltaub, Abner; Verdugo, Victor

doi:10.1137/1.9781611975031.47

Cited by 13 publications

(12 citation statements)

References 46 publications

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“…The current best is a O(log log rank)-competitive algorithm by (Lachish 2014) and (Feldman, Svensson, and Zenklusen 2014). Other works on the matroid secretary problem include (Soto 2013;Im and Wang 2011;Gharan and Vondrák 2013;Ma, Tang, and Wang 2016;Soto, Turkieltaub, and Verdugo 2021).…”

Section: Related Workmentioning

confidence: 99%

Secretary Matching with Vertex Arrivals and No Rejections

Goyal

2022

AAAI

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Most prior work on online matching problems has been with the flexibility of keeping some vertices unmatched. We study three related online matching problems with the constraint of matching every vertex, i.e., with no rejections. We adopt a model in which vertices arrive in a uniformly random order and the edge-weights are arbitrary positive numbers. For the capacitated online bipartite matching problem in which the vertices of one side of the graph are offline and those of the other side arrive online, we give a 4.62-competitive algorithm when the capacity of each offline vertex is 2. For the online general (non-bipartite) matching problem, where all vertices arrive online, we give a 3.34-competitive algorithm. We also study the online roommate matching problem, in which each room (offline vertex) holds 2 persons (online vertices). Persons derive non-negative additive utilities from their room as well as roommate. In this model, with the goal of maximizing the sum of utilities of all persons, we give a 7.96-competitive algorithm. This is an improvement over the 24.72 approximation factor in prior work.

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Section: Related Workmentioning

confidence: 99%

Secretary Matching with Vertex Arrivals and No Rejections

Goyal

2022

AAAI

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“…The current best is a O(log log rank)-competitive algorithm by (Lachish 2014). Other works on the matroid secretary problem include (Soto 2013;Im and Wang 2011;Gharan and Vondrák 2013;Soto, Turkieltaub, and Verdugo 2021).…”

Section: Related Workmentioning

confidence: 99%

Secretary Matching With Vertex Arrivals and No Rejections

Goyal¹

2021

Preprint

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Most prior work on online matching problems has been with the flexibility of keeping some vertices unmatched. We study three related online matching problems with the constraint of matching every vertex, i.e., with no rejections. We adopt a model in which vertices arrive in a uniformly random order and the non-negative edge-weights are arbitrary. For the capacitated online bipartite matching problem, in which the vertices of one side of the graph are offline and those of the other side arrive online, we give a 4.62-competitive algorithm when the capacity of each offline vertex is 2. For the online general (non-bipartite) matching problem, where all vertices arrive online, we give a 3.34-competitive algorithm. We also study the online roommate matching problem (Huzhang et al. 2017), in which each room (offline vertex) holds 2 persons (online vertices). Persons derive non-negative additive utilities from their room as well as roommate. In this model, with the goal of maximizing the social welfare, we give a 7.96competitive algorithm. This is an improvement over the 24.72 approximation factor in (Huzhang et al. 2017).

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“…For example, a major open problem in optimal stopping theory is the existence of O(1)-competitive policies for the matroid secretary problem. While Babaioff, Immorlica, and Kleinberg [Babaioff et al, 2007] conjectured the existence of such a policy, and O(1)-competitve policies are known for many special cases (see, e.g., Soto et al [2021]), the state-of-the-art for general matroids is a O(log log(rank))competitive policy due to Feldman et al [2014], Lachish [2014]. In stark contrast, Kleinberg and Weinberg [2012] give an optimal 2-competitive policy for the related matroid prophet inequality problem under full distributional knowledge.…”

Section: From α-Partition To Single-sample Prophet Inequalitiesmentioning

confidence: 99%

Single-Sample Prophet Inequalities via Greedy-Ordered Selection

Caramanis¹,

Dütting²,

Faw³

et al. 2021

Preprint

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We study single-sample prophet inequalities (SSPIs), i.e., prophet inequalities where only a single sample from each prior distribution is available. Besides a direct, and optimal, SSPI for the basic single choice problem [Rubinstein et al., 2020], most existing SSPI results were obtained via an elegant, but inherently lossy reduction to order-oblivious secretary (OOS) policies [Azar et al., 2014]. Motivated by this discrepancy, we develop an intuitive and versatile greedy-based technique that yields SSPIs directly rather than through the reduction to OOSs. Our results can be seen as generalizing and unifying a number of existing results in the area of prophet and secretary problems. Our algorithms significantly improve on the competitive guarantees for a number of interesting scenarios (including general matching with edge arrivals, bipartite matching with vertex arrivals, and certain matroids), and capture new settings (such as budget additive combinatorial auctions). Complementing our algorithmic results, we also consider mechanism design variants. Finally, we analyze the power and limitations of different SSPI approaches by providing a partial converse to the reduction from SSPI to OOS given by Azar et al.

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Strong Algorithms for the Ordinal Matroid Secretary Problem

Cited by 13 publications

References 46 publications

Secretary Matching with Vertex Arrivals and No Rejections

Secretary Matching with Vertex Arrivals and No Rejections

Secretary Matching With Vertex Arrivals and No Rejections

Single-Sample Prophet Inequalities via Greedy-Ordered Selection

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