Optimization problems in correlated networks.

Q1 Mathematics

Computational Social Networks Pub Date : 2016-01-01 Epub Date: 2016-01-22 DOI:10.1186/s40649-016-0026-y

Song Yang, Stojan Trajanovski, Fernando A Kuipers

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引用次数: 7

Abstract

Background: Solving the shortest path and min-cut problems are key in achieving high-performance and robust communication networks. Those problems have often been studied in deterministic and uncorrelated networks both in their original formulations as well as in several constrained variants. However, in real-world networks, link weights (e.g., delay, bandwidth, failure probability) are often correlated due to spatial or temporal reasons, and these correlated link weights together behave in a different manner and are not always additive, as commonly assumed.

Methods: In this paper, we first propose two correlated link weight models, namely (1) the deterministic correlated model and (2) the (log-concave) stochastic correlated model. Subsequently, we study the shortest path problem and the min-cut problem under these two correlated models.

Results and conclusions: We prove that these two problems are NP-hard under the deterministic correlated model, and even cannot be approximated to arbitrary degree in polynomial time. However, these two problems are solvable in polynomial time under the (constrained) nodal deterministic correlated model, and can be solved by convex optimization under the (log-concave) stochastic correlated model.

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关联网络中的优化问题。

背景:解决最短路径和最小切割问题是实现高性能和鲁棒性通信网络的关键。这些问题经常在确定性和不相关的网络中进行研究，既包括它们的原始公式，也包括一些受约束的变体。然而，在现实世界的网络中，由于空间或时间原因，链路权重(例如，延迟、带宽、故障概率)通常是相关的，并且这些相关的链路权重在一起以不同的方式表现，并不总是像通常假设的那样是相加的。方法:本文首先提出了两个相关的环节权重模型，即:(1)确定性相关模型和(2)(log-凹)随机相关模型。随后，我们研究了这两种相关模型下的最短路径问题和最小割问题。结果与结论:我们证明了这两个问题在确定性相关模型下是np困难的，甚至不能在多项式时间内逼近到任意程度。然而，这两个问题在(约束)节点确定性相关模型下可在多项式时间内求解，而在(对数-凹)随机相关模型下可通过凸优化求解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Social Networks Mathematics-Modeling and Simulation

自引率

0.00%

发文量

审稿时长

13 weeks

期刊介绍： Computational Social Networks showcases refereed papers dealing with all mathematical, computational and applied aspects of social computing. The objective of this journal is to advance and promote the theoretical foundation, mathematical aspects, and applications of social computing. Submissions are welcome which focus on common principles, algorithms and tools that govern network structures/topologies, network functionalities, security and privacy, network behaviors, information diffusions and influence, social recommendation systems which are applicable to all types of social networks and social media. Topics include (but are not limited to) the following: -Social network design and architecture -Mathematical modeling and analysis -Real-world complex networks -Information retrieval in social contexts, political analysts -Network structure analysis -Network dynamics optimization -Complex network robustness and vulnerability -Information diffusion models and analysis -Security and privacy -Searching in complex networks -Efficient algorithms -Network behaviors -Trust and reputation -Social Influence -Social Recommendation -Social media analysis -Big data analysis on online social networks This journal publishes rigorously refereed papers dealing with all mathematical, computational and applied aspects of social computing. The journal also includes reviews of appropriate books as special issues on hot topics.