Navigation in spatial networks: A survey

The study on the navigation process in spatial networks has attracted much attention in recent years due to the universal applications in real communication networks. This article surveys recent advances of the navigation problem in spatial networks. Due to the ability to overcome scaling limitations in utilizing geometric information for designing navigation algorithms in spatial networks, we summarize here several important navigation algorithms based on geometric information on both homogeneous and heterogeneous spatial networks. Due to the geometric distance employed, the cost associated with the lengths of additional long-range connections is also taken into account in this survey. Therefore, some contributions reporting how the distribution of long-range links' lengths affects the average navigation time are summarized. We also briefly discuss two other related processes, i.e. the random walk process and the transportation process. Finally, a few open discussions are included at the end of this survey.