You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
We study revenue maximization through sequential posted price mechanisms (SPMs) in single-dimensional settings with n buyers, and independent but not necessarily identical value distributions. We construct our SPMs by considering two simple pricing schemes: one that imitates Myerson's mechanism via taxation principle, and the other that posts a uniform price. We design a factor revealing LP that crisply captures the approximation factor of this SPM. In the H-units setting, our SPM yields the first improvement in approximation over the correlation-gap-based approximation factor from over eight years ago (Yan 2011). In the position auction setting, our SPM yields the first higher-than 1-1 e approximation factor. In the 1-unit setting, our SPM yields better than the current best known approximation factor for small values of the number of buyers n. Our results on SPMs immediately imply improved performance guarantees for the equivalent free-order prophet inequality problem. In the recent surge of results that show an improvement over 1-1 e for SPMs, ours is the only technique that generalizes beyond the 1-unit setting, and yields the first improvement over long established approximation factors in several settings.

Cited Abstract(s):
[1]: In the Prophet Secretary problem, samples from a known set of probability distributions arrive one by one in a uniformly random order, and an algorithm must irrevocably pick one of the samples as soon as it arrives. The goal is to maximize the expected value of the sample picked relative to the expected maximum of the distributions. This is one of the most simple and fundamental problems in online decision making that models the process selling one item to a sequence of costumers. For a closely related problem called the Prophet Inequality where the order of the random variables is adversarial, it is known that one can achieve in expectation 1 2 of the expected maximum, and no better ratio is possible. For the Prophet Secretary problem, that is, when the variables arrive in a random order, (2015) showed that one can actually get 1-1 e of the maximum. The 1-1 e bound was recently extended to more general settings by (2018). Given these results, one might be tempted to believe that 1-1 e is the correct bound. We show that this is not the case by providing an algorithm for the Prophet Secretary problem that beats the 1-1 e bound and achieves 1-1 e+1 400 times the expected maximum. We also prove a hardness result on the performance of algorithms under a natural restriction which we call deterministic distribution-insensitivity.
false Moved these two paragraphs here. Todo Finally, we compare our result with the results of [1] . Though they have a worse factor, their posted price result is applicable for a more general setting: i.e., applicable both for a fixed-seller-chosen ordering of buyers, and random ordering of buyers, whereas our posted pricing result is applicable only for a fixed-seller-chosen-ordering of buyers (namely, descending order of prices). While the random order setting is more general, note that a random order model for posted pricing does not give any additional benefit over the fixed-ordering when it comes to approximation for second price auctions with eager reserves.