(非)规模经济下的近似广义网络设计及其在能源效率中的应用

Y. Emek, S. Kutten, R. Lavi, Yangguang Shi
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引用次数: 4

摘要

在广义网络设计(GND)问题中,将一组资源(非排他性地)分配给多个请求。每个请求都将其权重贡献给它所使用的资源,然后通过特定于资源的成本函数将资源上的总负载转换为它所产生的成本。在能源效率应用的推动下,最近人们对使用成本函数的GND越来越感兴趣,这些成本函数表现出(非)规模经济((D)oS),即,成本函数对于小负载来说是次相加的,对于大负载来说是超相加的。本文从各个方面推进了现有文献关于(D)oS代价函数的GND问题的近似算法:(1)虽然现有的结果局限于路由请求在无向图中,用图的边识别资源,目前的文章提出了一个通用的近似框架,产生近似结果更广泛的请求族(包括各种类型的斯坦纳树和斯坦纳森林请求)在有向图和无向图中,其中的资源可以用边或顶点识别;(2)虽然现有的结果假设请求对其使用的每个资源贡献相同的权重,但我们的近似框架允许不相关的权重,从而为具有(D)oS成本函数的不相关并行机调度问题提供了第一个非平凡的近似;(3)现有的大多数逼近算法都是基于凸规划的,而我们的逼近框架是完全组合的,并且在强多项式时间内运行;(4)本文中考虑的(D)oS成本函数族比现有文献中考虑的更一般,为实际节能场景提供了更准确的抽象;(5)我们用(D)oS成本函数获得GND的第一个近似比率,该函数仅取决于资源技术的参数,而不随资源数量、请求数量或其权重而增长。我们的近似框架的设计在很大程度上依赖于Roughgarden的平滑工具箱[43],从而证明了该工具箱在近似算法领域的可能有用性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Approximating Generalized Network Design under (Dis)economies of Scale with Applications to Energy Efficiency
In a generalized network design (GND) problem, a set of resources are assigned (non-exclusively) to multiple requests. Each request contributes its weight to the resources it uses and the total load on a resource is then translated to the cost it incurs via a resource-specific cost function. Motivated by energy efficiency applications, recently, there is a growing interest in GND using cost functions that exhibit (dis)economies of scale ((D)oS), namely, cost functions that appear subadditive for small loads and superadditive for larger loads. The current article advances the existing literature on approximation algorithms for GND problems with (D)oS cost functions in various aspects: (1) while the existing results are restricted to routing requests in undirected graphs, identifying the resources with the graph’s edges, the current article presents a generic approximation framework that yields approximation results for a much wider family of requests (including various types of Steiner tree and Steiner forest requests) in both directed and undirected graphs, where the resources can be identified with either the edges or the vertices; (2) while the existing results assume that a request contributes the same weight to each resource it uses, our approximation framework allows for unrelated weights, thus providing the first non-trivial approximation for the problem of scheduling unrelated parallel machines with (D)oS cost functions; (3) while most of the existing approximation algorithms are based on convex programming, our approximation framework is fully combinatorial and runs in strongly polynomial time; (4) the family of (D)oS cost functions considered in the current article is more general than the one considered in the existing literature, providing a more accurate abstraction for practical energy conservation scenarios; and (5) we obtain the first approximation ratio for GND with (D)oS cost functions that depends only on the parameters of the resources’ technology and does not grow with the number of resources, the number of requests, or their weights. The design of our approximation framework relies heavily on Roughgarden’s smoothness toolbox [43], thus demonstrating the possible usefulness of this toolbox in the area of approximation algorithms.
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