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Vì vậy, xác suất của việc tìm kiếm một nút di động gần đến trung tâm của R là cao hơn hơn so với xác suất của việc tìm kiếm các nút trên ranh giới. Điều này có nghĩa rằng các nút di động đóng góp một phần không đều để phân phối tiệm cận nút không gian được tạo ra bởi RWP di động, mà chúng ta biểu thị bởi Fm | 112 LOCATION-BASED TOPOLOGY CONTROL of this issue the authors of Li et al. 2003 propose two techniques for avoiding this inconvenience i enforcing all unidirectional links in GLMST to become bidirectional or ii deleting all the unidirectional links in GLMST. If technique i is used the obtained graph is the symmetric supergraph of the original topology which is denoted as g mst if technique ii is used we obtain the symmetric subgraph of the original topology which we caU gLmst- Note that which one of the g mst and the G MST topology is to be preferred depends on the application scenario the former topology is relatively dense and it thus keeps more routing redundancy which is useful to balance the traffic load and to improve fault tolerance the latter topology is very sparse and it should be used when the expected network traffic is quite low. To convert GLMST into either g mst or G MST each node u after Phase 3 of the algorithm probes all the nodes in N u to find out whether the corresponding link is unidirectional. In case it is the link is either removed technique ii or the neighbor node is notified to add the reverse edge technique i . Note that in case the probed link u v is unidirectional node u is not in N v so node v does not know which transmit power to use to the send the reply message to u. This problem can be easily solved by piggybacking the transmit power mpv used by u to send the probe message in the message itself. Given the assumption of symmetric wireless medium using power mpv is sufficient for node v to reach node u. Protocol LMST is summarized in Figure 10.7. 10.2.2 Protocol analysis In Li et al. 2003 it is proven that the topology produced by LMST has the following properties 1. it preserves connectivity in the worst case 2. it has maximal logical node degree equal to 6 3. it can be computed in a fully distributed and localized fashion in particular computing Glmst requires sending only n messages overall n is the number of network nodes . .
