La Comunicación Química entre insectos.

In this thesis, a compact-trie-based k-nearest-neighbor search method is proposed. Through the k-nearest-neighbor search performance comparison against the brute-force based and the k-d tree based methods, the compact-trie-based method did show consistent performance superiority. The intrinsic relationship between the grid partitioning and the Cartesian coordinates of spatial points composed of positive decimal numbers, and the natural space partitioning by a compact trie constructed from the modified Cartesian coordinates of spatial points composed of positive decimal numbers inspired me to devise the compact-trie-based method.

In this pilot project so far, it has been shown that the compact-trie-based method performed better than the brute-force based and the k-d tree based methods in tests, searching the k nearest neighbors for a given two-dimensional spatial point within one million two-dimensional spatial points. More theoretic work needs to be done to prove the better performance of the compact-trie-based method in theory. And the k-nearest- neighbor search performance comparison result needs to be verified with more robust tests and using well-established and well-recognized standard libraries.

It is worth mentioning that the different search schemes employed in the compact- trie-based method and the k-d tree based method may have a significant role responsible for the performance difference. It would be ideal if the performance comparison was carried out while the two methods employed the same search scheme. Applying the best- first search scheme to the k-d tree based method seems promising, though maintaining the priority queue for the non-terminal nodes traversed seems not computationally cost-

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effective at the first sight because the k-d tree is a binary tree and any non-terminal node of the k-d tree has two and only two child nodes. Applying the best-first search scheme to the compact-trie-based method seems relatively not that promising because for each non- terminal node traversed, a list of its child nodes sorted by their minimum distances to the query point may need to be created, which could be computationally expensive. It might be quite worthwhile to implement both and find out how they actually turn out.

So far, the implementation of the compact-trie-based method has limited the input to positive decimal numbers. Expanding the input to negative decimal numbers may just be a matter of conversion. And other numeral systems might be worthwhile exploring, especially the binary system because any information can be represented by bits or binary numbers, and bit-based storage and/or computing may be more efficient.

Last, it is more significant to explore the potential applicability of the compact- trie-based method to high-dimensional data, to tackle the curse of dimensionality.

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