Mathematics Department, Uppsala University, Lägerhyddsvägen 1, Uppsala 75106, Sweden.
Centre for Advanced Spatial Analysis, University College London, 90 Tottenham Court Road W1T4TJ London, United Kingdom.
Phys Rev E. 2017 Sep;96(3-1):032316. doi: 10.1103/PhysRevE.96.032316. Epub 2017 Sep 27.
The costs associated to the length of links impose unavoidable constraints to the growth of natural and artificial transport networks. When future network developments cannot be predicted, the costs of building and maintaining connections cannot be minimized simultaneously, requiring competing optimization mechanisms. Here, we study a one-parameter nonequilibrium model driven by an optimization functional, defined as the convex combination of building cost and maintenance cost. By varying the coefficient of the combination, the model interpolates between global and local length minimization, i.e., between minimum spanning trees and a local version known as dynamical minimum spanning trees. We show that cost balance within this ensemble of dynamical networks is a sufficient ingredient for the emergence of tradeoffs between the network's total length and transport efficiency, and of optimal strategies of construction. At the transition between two qualitatively different regimes, the dynamics builds up power-law distributed waiting times between global rearrangements, indicating a point of nonoptimality. Finally, we use our model as a framework to analyze empirical ant trail networks, showing its relevance as a null model for cost-constrained network formation.
链路长度相关的成本对自然和人工运输网络的发展施加了不可避免的限制。当未来的网络发展无法预测时，同时最小化建设和维护连接的成本是不可能的，这需要竞争的优化机制。在这里，我们研究了一个由优化泛函驱动的单参数非平衡模型，该泛函定义为建设成本和维护成本的凸组合。通过改变组合的系数，该模型在全局和局部长度最小化之间进行插值，即最小生成树和一个称为动态最小生成树的局部版本之间进行插值。我们表明，在这个动态网络的集合中，成本平衡是网络总长度和传输效率之间出现权衡以及最优构建策略出现的充分条件。在两个定性不同的区域之间的转变中，动力学在全局重排之间建立了幂律分布的等待时间，表明存在非最优点。最后，我们使用我们的模型作为一个框架来分析经验蚂蚁轨迹网络，展示了它作为成本约束网络形成的零模型的相关性。
