Beating Greedy for Stochastic Bipartite Matching

Gamlath, Buddhima; Kale, Sagar; Svensson, Ola

doi:10.1137/1.9781611975482.176

Cited by 28 publications

(36 citation statements)

References 25 publications

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“…al. [8] further improves approximation guarantees for the generalized Pandora's box problem with matching constraints.…”

Section: Additional Discussion Of Related Workmentioning

confidence: 93%

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Delegated Pandora's box

Curtis¹,

Dughmi²,

Patel³

2022

Preprint

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In delegation problems, a principal does not have the resources necessary to complete a particular task, so they delegate the task to an untrusted agent whose interests may differ from their own. Given any family of such problems and space of mechanisms for the principal to choose from, the delegation gap is the worst-case ratio of the principal's optimal utility when they delegate versus their optimal utility when solving the problem on their own. In this work, we consider the delegation gap of the generalized Pandora's box problem, a search problem in which searching for solutions incurs known costs and solutions are restricted by some downward-closed constraint. First, we show that there is a special case when all random variables have binary support for which there exist constant-factor delegation gaps for matroid constraints. However, there is no constant-factor delegation gap for even simple non-binary instances of the problem. Getting around this impossibility, we consider two variants: the free-agent model, in which the agent doesn't pay the cost of probing elements, and discounted-cost approximations, in which we discount all costs and aim for a bicriteria approximation of the discount factor and delegation gap. We show that there are constant-factor delegation gaps in the free-agent model with discountedcost approximations for certain downward closed constraints and constant discount factors. However, constant delegation gaps can not be achieved under either variant alone. Finally, we consider another variant called the shared-cost model, in which the principal can choose how costs will be shared between them and the agent before delegating the search problem. We show that the shared-cost model exhibits a constant-factor delegation gap for certain downward closed constraints. * supported by NSF Grants CCF-1350900 and CCF-2009060. † supported by NSF CAREER Award CCF-1350900 and NSF Grant CCF-2009060. ‡ supported by NSF Grants CCF-1350900 and CCF-2009060. 1 In particular, a mechanism design problem without money.

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“…al. [8] further improves approximation guarantees for the generalized Pandora's box problem with matching constraints.…”

Section: Additional Discussion Of Related Workmentioning

confidence: 93%

“…Inequality (8) holds because Pr[agent finds a feasible i ∈ V ] is bounded by 1. We can further bound E[DEL R | agent finds a feasible i ∈ V ] by assuming that the agent proposes element i ∈ V with X i = √ n as long as it exists.…”

Section: Shared-cost Modelmentioning

confidence: 99%

Delegated Pandora's box

Curtis¹,

Dughmi²,

Patel³

2022

Preprint

View full text Add to dashboard Cite

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“…To our knowledge, the only general online rounding method other than independent rounding is the online contention resolution schemes initiated by Feldman et al [17] and further developed by Adamczyk and W lodarczyk [1], Lee and Singla [24], and Dughmi [11,12]. It has found applications mainly in online problems with stochastic information, such as prophet inequality [14,17], posted pricing [17], stochastic probing [17], and stochastic matching [14,18,19].…”

Section: Other Related Workmentioning

confidence: 99%

Improved Online Correlated Selection

Gao

Huang

et al. 2021

Preprint

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This paper studies the online correlated selection (OCS) problem introduced by Fahrbach, Huang, Tao, and Zadimoghaddam (2020) to get the first edge-weighted online bipartite matching algorithm that breaks the 0.5 barrier. Suppose that we receive a pair of elements in each round and select one of them. Can we select with negative correlation to be more effective than independent random selections? Our contributions are threefold. For semi-OCS, which considers the probability that an element remains unselected after appearing in k rounds, we give an optimal algorithm that minimizes this probability for all k. It leads to 0.536-competitive unweighted and vertex-weighted online bipartite matching algorithms that randomize over only two options in each round, improving the previous 0.508-competitive ratio by Fahrbach et al. (2020). Further, we give the first multi-way semi-OCS that allows an arbitrary number of elements with arbitrary masses in each round. As an application, it rounds the Balance algorithm in unweighted and vertex-weighted online bipartite matching to get a 0.593-competitive ratio. This is the first algorithm other than Ranking whose competitive ratio is beyond the 0.5 + ǫ regime. Finally, we study OCS, which further considers the probability that an element is unselected in any subset of rounds. We prove that the optimal "level of negative correlation" is between 0.167 and 0.25, improving the previous bounds of 0.109 and 1 by Fahrbach et al. (2020). Our OCS gives a 0.519-competitive edge-weighted online bipartite matching algorithm, improving the previous 0.508-competitive ratio by Fahrbach et al. (2020).

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“…Query-Commit. Motivated in part by the application of kidney exchange, there is a large body of literature studying a variant of stochastic matching known as the query-commit problem [1,7,9,14,17,21,40]. Here, edges have fixed realization probabilities and can be queried in sequence, with the constraint that successful edges queried must be accepted, and accepted edges must form a matching.…”

Section: Relationship With Prior Workmentioning

confidence: 99%

Decentralized Matching in a Probabilistic Environment

Jeloudar

Pollner

et al. 2021

Proceedings of the 22nd ACM Conference on Economics and Computation

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We consider a model for repeated stochastic matching where compatibility is probabilistic, is realized the first time agents are matched, and persists in the future. Such a model has applications in the gig economy, kidney exchange, and mentorship matching.We ask whether a decentralized matching process can approximate the optimal online algorithm. In particular, we consider a decentralized stable matching process where agents match with the most compatible partner who does not prefer matching with someone else, and known compatible pairs continue matching in all future rounds. We demonstrate that the above process provides a 0.316-approximation to the optimal online algorithm for matching on general graphs. We also provide a 1 /7-approximation for many-to-one bipartite matching, a 1 /11-approximation for capacitated matching on general graphs, and a 1 /2 -approximation for forming teams of up to agents. Our results rely on a novel coupling argument that decomposes the successful edges of the optimal online algorithm in terms of their round-by-round comparison with stable matching.

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Beating Greedy for Stochastic Bipartite Matching

Cited by 28 publications

References 25 publications

Delegated Pandora's box

Delegated Pandora's box

Improved Online Correlated Selection

Decentralized Matching in a Probabilistic Environment

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