Alexander Suvorov: A Structural-Statistical Approach to NP-Complete Problems
Novel structural-statistical approach that transforms NP-complete problem-solving from exhaustive search to systematic decomposition into positions, candidates, and hypotheses, followed by parallel investigation and statistical synthesis.
This research paper introduces the Position-Candidate-Hypothesis (PCH) paradigm as a novel theoretical approach to NP-complete problems. This work proposes a fundamental shift from traditional combinatorial search to structural-statistical analysis. The research explores the decomposition of problems into three interconnected components: positions, candidates, and hypotheses, followed by statistical integration. This work presents a new perspective on computational problem-solving that emphasizes structural analysis and pattern recognition over exhaustive search methods. The paradigm suggests potential pathways for more efficient approaches to classical NP-complete problems including SAT, Hamiltonian Path, and Graph Coloring.
PCH uses n hypotheses, n positions, and n candidates per position for problems of size n.