生成具有最小平均最短路径距离的高效网络
Efficient generation of networks with minimal average shortest-path distance
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中文总结 AI 辅助
本文针对给定度序列的网络，提出一种先连高度节点再按标准配置模型加边的快速算法，可将真实网络全对最短路径平均降低20%，计算成本远低于模拟退火，适用于大规模系统
中文摘要 AI 辅助
设计能最小化距离且满足结构约束的网络，是交通、通信和生物系统中的基础任务。本文针对给定度序列，研究如何找到具有最小可能平均最短路径长度的网络结构。对于树结构，可在线性时间内得到精确解，但一旦网络中允许存在环，该优化问题就会变得计算上不可行。我们提出一种快速算法，用于构造这类度约束的距离最小化问题的近似解：首先在高度节点之间创建边，然后按照标准配置模型的规则放置额外连接。尽管该算法十分简单，但在对合成度序列和真实度序列的系统实验中，其表现出优异性能，尤其对呈现中等异质性的合成度序列效果显著。当应用于真实网络的度序列时，该算法能将真实结构的全对最短路径平均降低20%。我们对小型网络进行验证，将本算法生成网络的最短路径距离与模拟退火优化得到的结果对比，发现尽管模拟退火能得到稍优的结构，但本算法能以低得多的计算成本提供几乎相同的解，使其成为大规模系统相关应用中的可靠方法。
英文摘要
Designing networks that minimize distances and satisfy structural constraints is a fundamental task across transportation, communication, and biological systems. Here, we consider the problem of finding, for a given degree sequence, the network structure displaying the smallest possible average shortest-path length. While exact solutions are available in linear time for trees, such an optimization problem becomes computationally infeasible as soon as loops are allowed in the networks. We propose a fast algorithm to construct approximate solutions to such a degree-constrained distance-minimization problem. Accordingly, edges are first created between high-degree nodes; then, additional connections are placed following the rules of the standard configuration model. In spite of its simplicity, the algorithm displays outstanding performance as demonstrated in our systematic experiments on both synthetic and real degree sequences. Our method is particularly effective on synthetic degree sequences displaying medium levels of heterogeneity. When applied to degree sequences of real networks, the proposed algorithm is able to reduce the all-pair shortest path of real structures by 20%, on average. We perform a validation on small-sized networks, where we compare the shortest-path distance of the networks generated with our algorithm against those obtained via simulated annealing optimization. Although simulated annealing yields slightly better structures, our proposed algorithm provides nearly identical solutions at a substantially lower computational cost, making it a solid method in applications concerning large-scale systems.
