# A Multi-Dimension Spatial Method for Topology Awareness and Multipath Generating
## 1 Introduction  
Various innovative internet applications are emerging thanks to the network infrastructures with ever growing quality, and, in turn, applications are demanding higher transmission capability to achieve better quality of experience (QoE). Although underlay networks are usually of good performance (e.g., high bandwidth, short latency), it is still challenging to guarantee end-to-end QoE, partially due to the \"best-effort\" layer-3 routing mechanism. According to 3 GPP (3 rd Generation Partnership Project), the conversational applications [1], e.g., real-time video conversation, demand not only specific end-to-end bidirectional bandwidth and delay, but also smooth procedure. The end-to-end QoE is vulnerable to link abnormality, e.g., outage and congestion, which happen randomly in underlay networks and are difficult to overcome using the single path transmission mode [2]. Therefore, the multipath transmission methodology has been coming up as a preventive or remedial measure to strengthen the end-to-end transmission quality. The distinct advantage of multipath transmission is that it aggregates transmission capabilities of multiple paths. On one hand, it expands the bandwidth by concurrently exploiting redundant links. On the other hand, it weakens the negative influence on the end-to-end transmission brought by link abnormality from a certain path. We mainly attribute this advantage to the uncorrelation of multiple paths, and name it multipath diversity. From the perspective of which part of networks multipath transmission enhances, we classify the studies of multipath transmission into two categories, namely,(i) on the end-host side, (ii) operating the intermediate network, and (i) some improved studies of multipath transmission control protocol (MPTCP) represent the enhancement on the end part [3], due to the fact that it focuses on optimizing the end flow control and schedule by using paths provided by multi-homed hosts. Actually, the multi-homed scenario is not common for most end devices. (ii) In [2], multipath diversity is improved in the intermediate networks on the internet protocol (IP) layer, while some modification has to be imposed on network infrastructures, e.g., router. Alternatively, overlay relays are adopted to redirect network traffic to multiple overlay paths as in [4; 5; 6; 7; 8]. In this paper, we mainly consider relevant two issues of generating multiple relay-based paths on overlay networks, namely (1) the topology match between overlay and underlay networks, and (2) generating multiple paths with high path diversity. (1) The topology match between overlay and underlay networks is a classical and still challenging issue for designing network architectures and deploying applications on overlay networks due to the characteristics of traditional TCP/IP protocol stacks. The mismatch problem is likely to result in transmission degradation for end users and low link utilization for bearing networks. We have analyzed the potentially serious consequences of topology mismatch for transmission in [9] including unacceptable large transmission delay and useless redirected network traffic. An efficient and widely studied methodology to solve the mismatch problem is topology awareness and a representative method to improve topology awareness for overlay networks is network positioning [10; 11; 12]. Based on the measure results, the overlay nodes are positioned with network coordinates in a coordinate system. While we discover that the underlay networks are complicated thanks to the abundant deployments of bearing networks from multiple Internet Service Providers (ISPs), the complicated bearing networks have some features of a complex network, and a main feature is that the networks devices are deployed in a cascade manner [13; 14]. For example, there exist various autonomous systems (AS) and they might cover overlapping geographic areas and be interconnected in several locations.