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arXiv · 2311.10965

(Nearest) Neighbors You Can Rely On: Formally Verified k-d Tree Construction and Search in Coq

Nadeem Abdul Hamid
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Abstract

The k-d tree is a classic binary space-partitioning tree used to organize points in k-dimensional space. While used in computational geometry and graphics, the data structure has a long history of application in nearest neighbor search. The objective of the nearest neighbor search problem is to efficiently find the closest point(s) to a given query point, and is the basis, in turn, of common machine learning techniques. We present in this paper a case study in the certified implementation, using the Coq proof assistant, of k-d tree construction from a set of data and the accompanying K-nearest neighbors search algorithm. Our experience demonstrates an intuitive method for specifying properties of these algorithms using the notion of list permutations.

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BibTeXRIS

Nadeem Abdul Hamid. 2023-11-18. (Nearest) Neighbors You Can Rely On: Formally Verified k-d Tree Construction and Search in Coq. https://arxiv.org/abs/2311.10965

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