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arXiv 1907.03058cs.NI
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节点约束流量工程:理论与应用

Node-Constrained Traffic Engineering: Theory and Applications

George Trimponias, Yan Xiao, Xiaorui Wu, Hong Xu, Yanhui Geng

摘要:

流量工程(TE)是网络中的一项基本任务。传统上,流量可以采用连接源和目的地的任何路径。然而,诸如段路由之类的新兴技术使用经过预定的中间点集合的逻辑路径。受此启发,在这项工作中,我们介绍了节点约束TE的问题,其中流量必须通过一组middlepoints,并研究其理论基础。我们表明,一般的节点约束TE,约束流量采取路径通过一个或多个middlepoints是NP-难的有向图,但强多项式的无向图,揭示了深刻的二分法之间的两种情况。我们还调查了流行的变种节点约束TE中间点之间使用最短路径,并表明,这个问题现在可以解决在弱多项式时间为固定数量的中间点。然而,如果我们将端到端的路径限制为非循环的,问题就变成了NP难的。这就解释了为什么现有的工作集中在计算易处理的变体。我们的工作的一个重要应用涉及流中心性的计算复杂性,首先在1991年由Freeman等人提出。[21]:我们证明了它是NP-难的有向图,但无向图的强多项式。最后,我们研究了一般节点约束TE中的中间点选择问题。我们引入了群流中心性作为多商品网络的解的概念,研究了它的复杂性,并证明了它是单调的,但不是子模的有向图和无向图。我们的工作提供了一个彻底的理论处理节点约束TE及其应用。

英文摘要:

Traffic engineering (TE) is a fundamental task in networking. Conventionally, traffic can take any path connecting the source and destination. Emerging technologies such as segment routing, however, use logical paths going through a predetermined set of middlepoints. Inspired by this, in this work we introduce the problem of node-constrained TE, where traffic must go through a set of middlepoints, and study its theoretical fundamentals. We show that the general node-constrained TE that constrains the traffic to take paths going through one or more middlepoints is NP-hard for directed graphs but strongly polynomial for undirected graphs, unveiling a profound dichotomy between the two cases. We additionally investigate the popular variant of node-constrained TE that uses shortest paths between middlepoints, and show that the problem can now be solved in weakly polynomial time for a fixed number of middlepoints. Yet if we constrain the end-to-end paths to be acyclic, the problem can become NP-hard. This explains why existing work focuses on the computationally tractable variant. An important application of our work concerns the computational complexity of flow centrality, first proposed in 1991 by Freeman et al. [21]: we show that it is NP-hard for directed but strongly polynomial for undirected graphs. Finally, we investigate the middlepoint selection problem in general node-constrained TE. We introduce group flow centrality as a solution concept for multi-commodity networks, study its complexity, and show that it is monotone but not submodular for both directed and undirected graphs. Our work provides a thorough theoretical treatment of node-constrained TE and its applications.

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