A Sublogarithmic Approximation for Tollbooth Pricing on Trees
研究了树上收费站定价问题，提出一种确定性算法，近似比达到O(log m / log log m)，优于现有结果，并揭示了该问题与单目标无限供给定价问题之间的计算复杂性差异。
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, and up until recently, also on the best ratio for paths (commonly known as the highway problem). 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.