New initialization for algorithms to solve Median String Problem

The median string problem is NP-hard under several formulations, being the most competitive heuristics those using perturbation-based iterative algorithms. The initial string and the policy to order possible edit operations are key to the efficiency of such approaches. In this work, we tackle both sub-problems. We hypothesized that a better starting point for the algorithm can reduce the number of edit distances computed to obtain the median string, improving time performance without degrading the quality of the solution. Regarding the starting point, we use the median of a few strings of the input, that is selected as the Half Space Proximal (HSP) neighbors of the median of the set. The HSP neighbors are simultaneously close to the center but also diverse among them. To validate these results, we present comparative experiments, attending mainly to the quality of the median obtained, the time to compute such median, and the number of edit distances computed.