Improving the linear kernel bounds

Determine whether the vertex bounds of 6k for Metric Violation Distance and 7k for Interval Metric Violation can be improved.

Background

The paper proves that Metric Violation Distance admits a solution-lifting kernel with at most 6k vertices and that its interval generalization, Interval Metric Violation, admits a kernel with at most 7k vertices. These bounds arise from a mandatory core, non-dominated witnesses, and a matching-based reduction.

The authors explicitly leave open whether the constants multiplying the parameter k in these kernel-size bounds can be reduced.