A new iterative algorithm for computing a quality approximate median of strings based on edit operations

• The approximated mean is computed through the successive improvements of a partial solution.
• A goodness index for edit operations is computed by multiplying their frequency by the cost.
• Partial solution is modified by applying edit operations with high goodness index.

This paper presents a new algorithm that can be used to compute an approximation to the median of a set of strings. The approximate median is obtained through the successive improvements of a partial solution. The edit distance from the partial solution to all the strings in the set is computed in each iteration, thus accounting for the frequency of each of the edit operations in all the positions of the approximate median. A goodness index for edit operations is later computed by multiplying their frequency by the cost. Each operation is tested, starting from that with the highest index, in order to verify whether applying it to the partial solution leads to an improvement. If successful, a new iteration begins from the new approximate median. The algorithm finishes when all the operations have been examined without a better solution being found. Comparative experiments involving Freeman chain codes encoding 2D shapes and the Copenhagen chromosome database show that the quality of the approximate median string is similar to benchmark approaches but achieves a much faster convergence.