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an agent aims to find a path on a hexagonal map with initial state s0 in the center and goal state s⋆ at the bottom as depicted below. The map is parametrized by the distance n ≥ 1 from s0 to any of the border cells (n = 3 in the depicted example). The agent can move from its current cell to any of the 6 adjacent cells,

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How can we find the number of node expansions performed by bfs without duplicate detection, and with duplicated detection as a function of n.

I know that the branching factor for the map would be 6 because the agent can move in 6 directions, and for a depth of k, we get O(b^k) = 6^n without duplicate detection, but what is the number of node expansion with duplicate detection with bfs.

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At first we must define what the OP has asked. He do not want to know, how an agent has to be programmed which acts intelligently in a hexagonal map, instead the question is about a meta-agent which is able to learn the behavior of other agents. The easiest form in doing so is a plan recognition. That means, the agent's actions are recorded, his branching strategy is parsed and as a result the node expansion ratio can be determined.

Plan recognition is equal to case-based learning. At first, the raw data of an agent needs to be recorded. Then the data gets annotated by a semantic tagger and a model is used for get the branching strategy. The model is also not about "Breadth first search" itself, but the question is about how to recognize a "Breadth first search" strategy performed by an agent. One option is to use a neural network for learning different models from the past, the other option is to create such a model manually with an ontology. In the easiest form, the parser counts the number of performed branches and calculates the ratio. A possible application would be a crawler detection algorithm which calculates the recursiveness of a bot.

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  • $\begingroup$ Thanks for the response, I just need to know what is the number of node expansion using Breadth first search with duplicate detection. $\endgroup$ – akano1 Jun 5 '18 at 14:26

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