# A Multi-Dimension Spatial Method for Topology Awareness and Multipath Generating
## 1 Introduction
The complicated bearing networks would lead to positioning inaccuracy, mainly due to the fact that the reference nodes for overlay nodes in different autonomous systems would cause delay deviation when overlay nodes in different autonomous systems are positioned together. Therefore, in this paper, in order to reduce topology match deviation and improve positioning accuracy, we try to simplify the complicated bearing networks and decompose the bearing network into multi-dimensions, namely horizontal dimension for intra-AS and vertical dimension for inter-AS. Firstly, we independently generate the coordinate-based topology view for overlay nodes in each autonomous system, i.e., the horizontal dimension. Then, we merge these views into a universal view by embedding exchange exports between autonomous systems, i.e., the vertical dimension. (2) Multipath diversity impacts the multipath transmission quality when capabilities of multiple concurrent paths with little correlation are aggregated. High multipath diversity helps improve the concurrent utilization of network links and minimizes the negative influence brought by an individual path, so that tolerance capability of network congestion and failure are improved [3; 15; 16]. In practice, it is more challenging to guarantee enough multipath diversity on overlay networks than in underlay bearing networks, mainly due to that there exists a little mechanism for overlay nodes in traditional networks to become aware of the precise underlay network topology. In this paper, we take advantages of abundant links existing in the complicated bearing networks and propose a multipath generating method. The motivation is as follows: In real-world underlay networks, various Internet Service Providers (ISPs) have deployed their own infrastructures of different scopes, so that there might exist redundant links between a pair of origin-destination hosts. An ideally typical scenario is that two paths between an origin-destination pair separately traverse two different service providers. Thus, based on the existing underlay link diversity, we hold the opinion that links through different service providers are more likely to be independent, and multiple paths consisting of independent links would gain high multipath diversity. On the basis of the multi-dimension topology match view in (1) above, we also design the multipath generating method from two dimensions, namely inter-AS (among autonomous systems) and intra-AS (among relay nodes in an autonomous system). Firstly, we use autonomous systems as the basic unit and try to redirect traffic to paths belonging to totally different autonomous systems; this is named inter-AS. While practically this ideal scenario is not always feasible, due to the fact that some geographic areas are not covered by multiple autonomous systems, in some areas, paths have to pass through the same autonomous systems. Then, we have to minimize (maximize) the multipath correlation (multipath diversity) in one autonomous system. We design some spatial mechanisms to improve multipath diversity, e.g., we use the cosine similarity (\"Deviation Angle\") to evaluate link correlation, and use \"Transmission Surface\" to constrain available nodes. After analyzing the above issues, we make the following contributions in this paper:  
(1) In order to improve network positioning accuracy for topology awareness, we decompose the bearing networks into a multi-dimension structure, namely intra-AS and inter-AS dimensions and design the multi-dimension topology view. (2) We design some spatial mechanisms to evaluate the correlation of first-hop links, and to constrain multipath generating. (3) We design an inter-AS and intra-AS multipath generating method to improve multipath diversity by taking advantages of underlay diversity. (4) We evaluate the multi-dimension spatial method on the OMNet++ simulation platform considering topologies generated with BRITE and brought from practical real-world networks. The remaining parts of this paper are arranged as follows.