arXiv subjects

Changryeol Lee

Publications and source records attributed to Changryeol Lee.

3 recordsLinked to original sources

arXiv2026

Implementation of Polynomial NP-Complete Algorithms Based on the NP Verifier Simulation Framework

While prior work established a verifier-based polynomial-time framework for NP, explicit deterministic machines for concrete NP-complete problems have remained elusive. In this paper, we construct fully specified deterministic certificate-oblivious verifier Turing machines for SAT and Subset-Sum within an improved NP verifier simulation framework. A key contribution of this work is the development of a functional implementation that bridges the gap between theoretical proofs and executable software. Our improved feasible-graph construction yields a theoretical reduction in the asymptotic polynomial degree, while enhanced edge extension mechanisms significantly improve practical execution speed. We show that these machines generate valid witnesses, extending the framework to deterministic FNP computation without increasing complexity. The complete Python implementation behaves in accordance with the predicted polynomial-time bounds, and the source code, along with sample instances, is available in a public online repository.

cs.CC↗

arXiv2025

Graph-Based Deterministic Polynomial Framwork for NP Problems

The P versus NP problem asks whether every language verifiable in polynomial time can also be decided in deterministic polynomial time. In this paper, we present a constructive proof that P=NP by introducing a universal, graph-based deterministic framework applicable to all NP problems without requiring reduction to an NP-complete problem. We model computational transitions as edges within a unified graph structure, where edges correspond to the steps of a deterministic verifier Turing machine for all possible certificates. Due to the overlap of edges among computation paths, the total cardinality of the edge set remains polynomially bounded. Furthermore, by employing a certificate--oblivious verifier Turing machine--whose head movement is independent of the certificate contents--we force all computation paths to align their edge transitions. A key feature of our approach is that each extension step enforces global consistency via a local infeasibility trimming tool. This mechanism systematically preserves valid NP paths that lead to the target edge under polynomial verification, ensuring the graph remains globally feasible at every stage without explicit enumeration. This represents a paradigm shift from searching over exponential certificates to the incremental extension of verified edges. Since our construction decides all NP problems in deterministic polynomial time, it provides a direct resolution to the P versus NP question and demonstrates that every NP problem can be solved in deterministic polynomial time via incremental graph edge extension.

cs.CC↗

arXiv2012

Single-Source Dilation-Bounded Minimum Spanning Trees

Given a set $S$ of points in the plane, a geometric network for $S$ is a graph $G$ with vertex set $S$ and straight edges. We consider a broadcasting situation, where one point $r \in S$ is a designated source. Given a dilation factor $δ$, we ask for a geometric network $G$ such that for every point $v \in S$ there is a path from $r$ to $v$ in $G$ of length at most $δ|rv|$, and such that the total edge length is minimized. We show that finding such a network of minimum total edge length is NP-hard, and give an approximation algorithm.

cs.CG↗