Year: 2025
Type: preprint
Abstract: We frame NP problems not as targets for mere statistical cleaning but for transformative reinterpretation prior to solving. To illustrate this idea, we present three representative preprocessing methods: Fourier-Guided Preprocessing (FGP), Laplace-Guided Preprocessing (LGP), and Entropy-Guided Preprocessing (EGP). These methods reshape instance structure through a signalization-domain adjustmentdiscrete remapping pipeline, exposing sharp shifts in solvability. On Subset Sum, all three alter the phasetransition profile; on SAT and 2-Coloring on 3uniform hypergraphs, continuous operators (FGP/LGP) may disrupt combinatorial consistency, whereas EGP preserves discreteness while shifting the location or widening the width of the transition region. These findings support a simple principle: transformation precedes computation. Preprocessing is thus recast as a guided lens that clarifies solvability transitions before any learning or search. Our contributions are: (i) a cross-domain comparison of the three methods under a unified perspective; (ii) evidence that, when combinatorial semantics must be preserved, EGP is a reliable baseline; and (iii) a modular formalization of FGP/LGP/EGP with a common interface for transplantation into preprocessing stages beyond NP tasks. We provide runnable code and experiment settings for reproducibility, and outline how learning-based components can be layered on these clarified inputs. Beyond NP problems, we envision this approach being extended to diverse complex systems, including physical signal processing, biological networks, and social systems.
Author: KEUNSOO YOON
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
OpenAlex ID: W4414364844
Cites:
Cited by:
Related to: