An Interesting Gadget for Chain Pair Simplification

In this paper we present an interesting gadget based on the chain pair simplification problem under the discrete Fr'echet distance (CPS-3F), which allows the construction of arbitrarily long paths that must be chosen in the simplification of the two curves. A pseudopolynomial time reduction from set partition is given as an example. For clarification, CPS-3F was recently shown to be in $\mathbf{\text{P}}$, and the reduction is merely to show how the gadget works.