By John Markus; Vin Zeluff; Electronics
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Each coordinator node sends a HELLO message and each noncoordinator node sends a CHECK message. Let be the average number of coordinator neighbors of a noncoordinator node. A noncoordinator node sends a CHECK REPLY message in response to a CHECK message if and only if there is no match between the coordinator neighbor lists of the noncoordinator nodes. In Span, each noncoordinator node sends one message and each coordinator node sends two messages. Therefore, the number of messages sent in each Tperiod interval is N + Nc .
3 The spanning subgraph G generated by MAXCOVSPAN provides the highest coverage among all spanning subgraphs of G that have the same number of nodes as G . PROOF In order to avoid case-by-case analysis, we prove this theorem using mathematical induction. Suppose G = (V, E) is the graph corresponding to the sensor network. Let Pi = (Vi , E i ) denote the partial (incomplete) spanning subgraph of size i generated by MAXCOVSPAN. Let Cov(Pi ) denote the coverage obtained with Pi . Consider the base case P1 = (v1 , φ), where v1 is any node selected at random.
Artificial locations rather than their real location to estimate the distance between them and a coordinator node. We refer to this scheme as either SCARE-10 or SCARE-20. 16 shows the results of these simulations. The simulations using SCARE-10 and SCARE-20 are based on incorrect estimation of the distance from the coordinators by the nodes. Consequently, the number of coordinators is different from the case when there is no error. However, the increase in the number of coordinators is negligible, while the decrease in coverage is found to be minimal.