In this research, we propose the nearest neighbor searching problem and we give an algorithm to solve the problem. Roughly speaking, the nearest neighbor searching problem is defined as follows: Give a text string T=t₁t₂…t_n and a pattern string P=p₁p₂…p_m, find all substrings in T whose edit distances with respect to P are the smallest among all substrings of T. Our algorithm is based upon two concepts: (1) There is a special property of dynamic programming matrix which is used to solve the approximate string matching problem. We call this property the small change property. (2) Values on the D matrix can be computed along the diagonals. Our experimental results showed that our algorithm is quite efficient.