Improved Online Contention Resolution for Matchings and Applications to the Gig Economy

Pollner, Tristan; Roghani, Mohammad; Saberi, Amin; Wajc, David

doi:10.1145/3490486.3538295

Cited by 7 publications

(3 citation statements)

References 1 publication

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“…They also first established a (1 − 1/e)-selectable RCRS for random-order edge arrivals in general graphs, using the same time-agnostic attenuation functions. [PRSW22] establish an alternate (1 − e −2 )/2selectable RCRS using the time-aware attenuation function of [LS18], and also break the barrier of (1 − e −2 )/2 for this problem. The state-of-the-art for this problem of random-order edge arrivals in general graphs (again using time-agnostic attenuation functions) is currently given by [MMG23].…”

Section: Further Discussion Of Related Workmentioning

confidence: 99%

“…This result does not appear to easily follow from modifying existing approaches to exploit independence. Indeed, both the (1 − e −2 )/2-selectable RCRS of [BGMS21] and the alternate proof of a (1 − e −2 )/2-selectable RCRS from [PRSW22] (based on the attenuation function of [LS18]) require defining explicit functions f e , and in fact are exactly 1 (1 − e −2 )/2-selectable on trees. By 1 This can be seen from a graph G = (V, E) with V = {ui, vi} n i=0 and E = {(u0, v0)} ∪ {(u0, ui), (v0, vi)} n i=1 .…”

Section: New Framework: Exact Selection In Continuous Timementioning

confidence: 99%

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On (Random-order) Online Contention Resolution Schemes for the Matching Polytope of (Bipartite) Graphs

MacRury¹,

Ma²,

Grammel³

2023

Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)

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We introduce a new approach for designing Random-order Contention Resolution Schemes (RCRS) via exact solution in continuous time. Given a function c(y) : [0, 1] → [0, 1], we show how to select each element which arrives at time y ∈ [0, 1] with probability exactly c(y). We provide a rigorous algorithmic framework for achieving this, which discretizes the time interval and also needs to sample its past execution to ensure these exact selection probabilities. We showcase our framework in the context of online contention resolution schemes for matching with random-order vertex arrivals. For bipartite graphs with two-sided arrivals, we design a (1 + e −2 )/2 ≈ 0.567-selectable RCRS, which we also show to be tight. Next, we show that the presence of short odd-length cycles is the only barrier to attaining a (tight) (1+e −2 )/2-selectable RCRS on general graphs. By generalizing our bipartite RCRS, we design an RCRS for graphs with odd-length girth g which is (1+e −2 )/2-selectable as g → ∞. This convergence happens very rapidly: for triangle-free graphs (i.e., g ≥ 5), we attain a 121/240 + 7/16e 2 ≈ 0.563-selectable RCRS. Finally, for general graphs we improve on the 8/15 ≈ 0.533-selectable RCRS of [FTW + 21] and design an RCRS which is at least 0.535-selectable. Due to the reduction of [EFGT22], our bounds yield a 0.535-competitive (respectively, (1 + e −2 )/2-competitive) algorithm for prophet secretary matching on general (respectively, bipartite) graphs under vertex arrivals.

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Section: Further Discussion Of Related Workmentioning

confidence: 99%

Section: New Framework: Exact Selection In Continuous Timementioning

confidence: 99%

On (Random-order) Online Contention Resolution Schemes for the Matching Polytope of (Bipartite) Graphs

MacRury¹,

Ma²,

Grammel³

2023

Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)

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“…More general feasibility constraints have also been studied in the random arrival order case, i.e. for matroids [AW20] and matchings [BGMS21,PRSW22].…”

Section: Related Workmentioning

confidence: 99%

Prophet Inequalities for Cost Minimization

Vasilis¹,

Mehta²

2022

Preprint

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Prophet inequalities for rewards maximization are fundamental results from optimal stopping theory with several applications to mechanism design and online optimization. We study the cost minimization counterpart of the classical prophet inequality due to Krengel, Sucheston, and Garling [KS77], where one is facing a sequence of costs X 1 , X 2 , . . . , X n in an online manner and must "stop" at some point and take the last cost seen. 1 Given that the X i 's are independent random variables drawn from known distributions, the goal is to devise a stopping strategy S (online algorithm) that minimizes the expected cost. The best cost possible is E [min i X i ] (offline optimum), achievable only by a prophet who can see the realizations of all X i 's upfront. We say that strategy S is an α-approximation to the prophet (α ≥ 1) ifWe first observe that if the X i 's are not identically distributed, then no strategy can achieve a bounded approximation, no matter if the arrival order is adversarial or random, even when restricted to n = 2 and distributions with support size at most two. 2 This leads us to consider the case where the X i 's are independent and identically distributed (I.I.D.). For the I.I.D. case, we give a complete characterization of the optimal stopping strategy. We show that it achieves a (distribution-dependent) constant-factor approximation to the prophet's cost for almost all distributions and that this constant is tight. In particular, for distributions for which the integral of the hazard rate 3 is a polynomial H(x) = k i=1 a i x di , where d 1 < • • • < d k , the approximation factor is λ(d 1 ), a decreasing function of d 1 , and is the best possible for H(x) = x d1 . Furthermore, when the hazard rate is monotonically increasing (i.e. the distribution is MHR), we show that this constant is at most 2, and this again is the best possible for the MHR distributions.For the classical prophet inequality for reward maximization, single-threshold strategies have been powerful enough to achieve the best possible approximation factor. Motivated by this, we analyze single-threshold strategies for the cost prophet inequality problem. We design a threshold that achieves a O (polylog n)-factor approximation, where the exponent in the logarithmic factor is a distribution-dependent constant, and we show a matching lower bound.We believe that our results may be of independent interest for analyzing approximately optimal (posted price-style) mechanisms for procuring items.

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Towards an Optimal Contention Resolution Scheme for Matchings

Pranav

Vondrák

2023

Lecture Notes in Computer Science

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Improved Online Contention Resolution for Matchings and Applications to the Gig Economy

Cited by 7 publications

References 1 publication

On (Random-order) Online Contention Resolution Schemes for the Matching Polytope of (Bipartite) Graphs

On (Random-order) Online Contention Resolution Schemes for the Matching Polytope of (Bipartite) Graphs

Prophet Inequalities for Cost Minimization

Towards an Optimal Contention Resolution Scheme for Matchings

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