公路收费定价的次对数近似
A Sublogarithmic Approximation for Highway and Tollbooth Pricing
摘要：
收费站问题的一个例子是由一个无向网络和一群一心一意的顾客组成的，每个顾客都有兴趣购买一条受个人预算约束的固定路径。目标是以最大化从所有客户获得的集体收入的方式为每个边缘分配单位价格。当成本在其预算范围内时，任何客户产生的收入等于其期望路径中的边的总价格;否则，该客户将不会购买任何边。我们的主要结果是一个确定性算法的收费亭问题的近似比为O（log m / log log m）的树，其中m表示在底层图的边缘数。这一发现改善了目前最好的性能保证树，由于Elbassioni等人。（SAGT '09），以及路径（通常称为公路问题），由于Balcan和Blum（EC '06）。另一个有趣的结果是在Demaine等人提出的一个合理的硬度假设（SODA '06）下，收费站对树木的定价与原始的单一无限供应定价原型问题之间的计算分离。
英文摘要：
An instance of the tollbooth problem consists of an undirected network and a collection of single-minded customers, each of which is interested in purchasing a fixed path subject to an individual budget constraint. The objective is to assign a per-unit price to each edge in a way that maximizes the collective revenue obtained from all customers. The revenue generated by any customer is equal to the overall price of the edges in her desired path, when this cost falls within her budget; otherwise, that customer will not purchase any edge. Our main result is a deterministic algorithm for the tollbooth problem on trees whose approximation ratio is O(log m / log log m), where m denotes the number of edges in the underlying graph. This finding improves on the currently best performance guarantees for trees, due to Elbassioni et al. (SAGT '09), as well as for paths (commonly known as the highway problem), due to Balcan and Blum (EC '06). An additional interesting consequence is a computational separation between tollbooth pricing on trees and the original prototype problem of single-minded unlimited supply pricing, under a plausible hardness hypothesis due to Demaine et al. (SODA '06).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
