小世界网络的扩展可导航性：确切结果和新见解
Extended navigability of small world networks: exact results and new insights
摘要：
网络的可导航性，即从任何其他顶点开始找到任何给定目的地顶点的能力，对它们的有用性至关重要。在2000年，Kleinberg证明了在小世界网络中可以实现最优的导航性，只要使用特殊的配方来建立长距离连接，并且使用贪婪算法来确保到达目的地。在这里，我们提供了一个精确的解决方案，这样的贪婪算法的渐近行为作为系统的参数的函数。我们的解决方案使我们能够表明，原来的要求，只有一个非常特殊的结构是最佳的，可以放宽取决于进一步的标准，如，例如，成本最小化，必须满足。
英文摘要：
Navigability of networks, that is the ability to find any given destination vertex starting from any other vertex, is crucial to their usefulness. In 2000 Kleinberg showed that optimal navigability could be achieved in small-world networks provided that a special recipe was used to establish long range connections, and that a greedy algorithm, that ensures that the destination will be reached, is used. Here we provide an exact solution for the asymptotic behavior of such a greedy algorithm as a function of the system's parameters. Our solution enables us to show that the original claim that only a very special construction is optimal can be relaxed depending on further criteria, such as, for example, cost minimization, that must be satisfied.
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