The Effect of Structure on Network Sample Clauses

The Effect of Structure on Network. Based Search‌ The search path for network based search forms a tree structure, where the root vertex is the agent searching for a service, every other vertex in the tree is an agent that is queried for a particular service, each edge is a branch of the search path, and the children of each vertex represent agents being queried. For an agent to query a single neighbour, two time steps elapse: one to send the query; and another for the response. The time required in a given network can thus be determined by the number of connections in the search tree. Suppose we have a search tree, as in Figure 6.6(a), such that below each vertex there are two branches: a binary tree. If we consider the root of the search tree to be level 0, then from level 0 to levels 1, 2, and 3 there are a total of 2, 6, and 14 edges in the search tree, respectively. Thus, for binary trees, from level zero to level or depth, d, there are 2d+1 − 2 edges in the search tree. More generally, with any regular number of branches from each vertex, where the search tree is d levels deep, and each vertex has b branches, we have the following number of edges: bd+1 − b b − 1 As network based search progressively searches 1 level deep, 2 levels, and so on, until d levels, as in Figures 6.6(a), (b), and (c), respectively, the total time needed to reach d levels can thus be calculated as follows:
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