An Interesting Gadget for Chain Pair Simplification

TL;DR

This paper introduces a novel gadget for chain pair simplification under the discrete Fréchet distance, demonstrating its ability to construct long paths and illustrating its application via a reduction from set partition.

Contribution

The paper presents a new gadget for CPS-3F that enables complex path constructions, clarifying the problem's structure and its relation to set partition.

Findings

Gadget allows arbitrarily long path constructions in CPS-3F.

Reduction from set partition demonstrates the gadget's utility.

CPS-3F is in P, as shown by recent results.

Abstract

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 \textbf{P}, and the reduction is merely to show how the gadget works.