## 2 Related Work  
In the traditional relay-node selection methods for VNET, the information of speed, acceleration, and location of neighbors, which is beneficial to the selection, is enclosed in a periodical beacon, e.g., the method in the known Greedy Perimeter Stateless Routing (GPSR) [15] and its novel methods. However, the interval of two successive beacons (100 ms) makes this information sacrifice its real-time features. The position-based multi-hop broadcast protocol (PMBP) [16] and the trinary partitioned black-burst-based broadcast protocol (3P3B) [17] take advantage of the information of local road structure (the straight road) to select the relay node without the prior knowledge of the neighbor location. However, in Ref. [18], the intersection is considered to develop the urban multi-hop broadcast protocol (UMB) and ad hoc multi-hop broadcast (AMB), as well as the binary-partition-assisted broadcast protocol (BPAB) in Ref. [19]. Based on the road structure, the above four methods partition the communication range into multi-segments and select the node in the final empty segment as the relay node. Consequently, these methods achieved a limited partition latency and relatively small contention latency. However, in the heavy or sparse traffic, these methods would deteriorate seriously. Meanwhile, there are many existing works to model and analyze the performance of the relay-node selection [20; 21; 22; 23]. However, efforts are still limited in the case of the typical crossroad and straight road. The literature [24] and [25] study the impact of the obstacles in the intersection and propose the network-coded intersection relaying and the selective intersection relaying to improve the performance in terms of PDR, respectively. More efforts need to be made in the study to select the node in realistic scenarios, not only a straight road and crossroad but also an atypical intersection and curved road. In our earlier work [13], an exponent-based partition method was proposed to select the relay node in a straight road. With the aid of the black burst (BB) (i.e., a channel-jamming signal), the communication range (\(R\)) of the sender is partitioned into \(N_{\text{part}}\) segments with \(N_{\text{iter}}\) iteration. Figure 1 shows an example with \((N_{\text{iter}},N_{\text{part}})=(2,3)\). In each iteration, the segment nearer to the border has a smaller width. The width of the \(i\)-th segment in the \(j\)-th iteration can be given as  
\[W_{\text{seg}}(j,i)=\frac{1}{A}\left[(1+A)^{\frac{\left((i-1)\text{ mod }N_{\text{part}}\right)+1}{N_{\text{part}}}}-(1+A)^{\frac{\left(i-1\right)\text{ mod }N_{\text{part}}}{N_{\text{part}}}}\right]W_{\text{seg}}\left(j-1,\left\lceil \frac{i}{N_{\text{part}}}\right\rceil\right) \tag{1}\]  
where \(A\) is a compression coefficient, and \(\left\lceil\bullet\right\rceil\) denotes the ceiling function. In our robust method [14], based on the closed-form expression of the performance in terms of the message dissemination speed, the optimal parameters of \(N_{\text{iter}}\), \(N_{\text{part}}\), \(N_{\text{A}}\) for EPBP are given. Moreover, a mini-black-burst-assisted mechanism (mini-BBM) is developed to reduce the partition latency in the low node density. The robust method performs a stable performance on the straight road. In this paper, the optimization of the exponent partition and mini-BBM also are adapted to explore a general relay-node selection on the intersection. For clear exposition, the primary notations throughout this paper are summarized in Table 1.