文章基本信息

标题：Approximate Pricing in Networks: How to Boost the Betweenness and Revenue of a Node
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作者：Ruben Brokkelkamp ; Sven Polak ; Guido Sch{"a}fer 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2019
卷号：149
页码：1-15
DOI：10.4230/LIPIcs.ISAAC.2019.13
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We introduce and study two new pricing problems in networks: Suppose we are given a directed graph G = (V, E) with non-negative edge costs (c_e)_{e in E}, k commodities (s_i, t_i, w_i)_{i in [k]} and a designated node u in V. Each commodity i in [k] is represented by a source-target pair (s_i, t_i) in V x V and a demand w_i>0, specifying that w_i units of flow are sent from s_i to t_i along shortest s_i, t_i-paths (with respect to (c_e)_{e in E}). The demand of each commodity is split evenly over all shortest paths. Assume we can change the edge costs of some of the outgoing edges of u, while the costs of all other edges remain fixed; we also say that we price (or tax) the edges of u. We study the problem of pricing the edges of u with respect to the following two natural objectives: (i) max-flow: maximize the total flow passing through u, and (ii) max-revenue: maximize the total revenue (flow times tax) through u. Both variants have various applications in practice. For example, the max flow objective is equivalent to maximizing the betweenness centrality of u, which is one of the most popular measures for the influence of a node in a (social) network. We prove that (except for some special cases) both problems are NP-hard and inapproximable in general and therefore resort to approximation algorithms. We derive approximation algorithms for both variants and show that the derived approximation guarantees are best possible.
关键词：Network pricing; Stackelberg network pricing; betweenness centrality; revenue maximization