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For practical applications, any neighborhood concept imposed on a finitepoint set P is not of any use if it cannot be computed efficiently. Thus, inthis paper, we give an introduction to the data structure of k-d trees, firstpresented by Friedman, Bentley, and Finkel in 1977. After a short introductionto the data structure (Section 1), we turn to the proof of efficiency byFriedman and his colleagues (Section 2). The main contribution of this paper isthe translation of the proof of Freedman, Bentley, and Finkel into modern termsand the elaboration of the proof.

The k-d tree data structure and a proof for neighborhood computation in expected logarithmic time