Polynomial Time Instances for the IKHO Problem

Figure 7

The subdivision on the 𝑘 dimension. A possible best solution 𝑥_opt is drawn. The black spots represent the insertions. It is simple to see that the value 𝑘_opt−|𝑠_opt| is a bound for the number of insertions placed at the right of 𝑠_opt, while 𝐾−𝑘_opt bounds the number of insertions at the left of the signature.