Batching and Optimal Multi-stage Bipartite Allocations

Feng, Yiding; Niazadeh, Rad

doi:10.2139/ssrn.3689448

Cited by 3 publications

(3 citation statements)

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“…We should mention, since the appearance of an early online version of our paper, there has been a few follow up work. Most importantly, Feng and Niazadeh (2020) extend our result for the two-stage (fractional) matching under adversarial arrival to K ∈ N stages using the idea of convex programming-based matching, showing an optimal competitive ratio of Γ(K) = 1 − (1 − 1 K ) K by carefully picking the convex program at each stage. Interestingly, as it has been shown in this paper, there is a uniquely identifiable sequence of polynomials of decreasing degrees, one for each stage, that can be used to regularize the maximum matching linear program to obtain this result.…”

Section: Optimum Onlinementioning

confidence: 53%

Two-stage Matching and Pricing with Applications to Ride Hailing

2020

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Section: Optimum Onlinementioning

confidence: 53%

Two-stage Matching and Pricing with Applications to Ride Hailing

2020

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“…Our dual-fitting style of analysis shares similarities with [13,30]. Another related recent line of work is on multi-stage bipartite allocations and matchings, where similar-inspirit primal-dual analysis frameworks are discovered using ideas from convex programming duality, e.g., [36,18,21].…”

Section: Introductionmentioning

confidence: 99%

Online Bipartite Matching with Reusable Resources

Delong¹,

Farhadi²,

Niazadeh³

et al. 2021

Preprint

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We study the classic online bipartite matching problem with a twist: offline nodes are reusable any number of times. Every offline node i becomes available d steps after it was assigned to. Nothing better than a 0.5-approximation, obtained by the trivial deterministic greedy algorithm, was known for this problem. We give the first approximation factor beating 0.5, namely a 0.505 approximation, by suitably adapting and interpreting the powerful technique of Online Correlated Selection.

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“…This conversion in the large capacity regime is quite straightforward and can be done by using standard independent randomized rounding techniques based on concentration bounds (e.g., seeFeng and Niazadeh, 2021).…”

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confidence: 99%