Complexity
- Building a static k-d tree from n points takes:
- O(n log2 n) time if an O(n log n) sort such as Heapsort is used to compute the median at each level;
- O(n log n) time if a complex linear-time median-finding algorithm such as the one described in Cormen et al. is used;
- O(kn log n) plus O(n log n) time if n points are sorted in each of k dimensions using an O(n log n) sort prior to building the k-d tree.
- Inserting a new point into a balanced k-d tree takes O(log n) time.
- Removing a point from a balanced k-d tree takes O(log n) time.
- Querying an axis-parallel range in a balanced k-d tree takes O(n1-1/k +m) time, where m is the number of the reported points, and k the dimension of the k-d tree.
Read more about this topic: K-d Tree
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