Closest Pair of Points Problem - Dynamic Closest-pair Problem

Dynamic Closest-pair Problem

The dynamic version for the closest-pair problem is stated as follows:

• Given a dynamic set of objects, find algorithms and data structures for efficient recalculation of the closest pair of objects each time the objects are inserted or deleted.

If the bounding box for all points is known in advance and the constant-time floor function is available, then the expected O(n) space data structure was suggested that supports expected-time O(log n) insertions and deletions and constant query time. When modified for the algebraic decision tree model, insertions and deletions would require O(log2 n) expected time. It is worth noting, though, that the complexity of the dynamic closest pair algorithm cited above is exponential in the dimension d, and therefore such an algorithm becomes less suitable for high-dimensional problems.