A special machine for solving NP-complete problems

Abstract

A specialized computer named as the Electronic Probe Computer (EPC) has been developed to address large-scale NP-complete problems. The EPC employs a hybrid serial/parallel computational model, structured around four main subsystems: a converting system, an input/output system, and an operating system. The converting system is a software component that transforms the target problem into the graph coloring problem, while the operating system is designed to solve these graph coloring challenges. Comprised of 60 probe computing cards, this system is referred to as EPC60. In tackling large-scale graph coloring problems with EPC60, 100 3-colorable graphs were randomly selected, each consisting of 2,000 vertices. The state-of-the-art mathematical optimization solver achieved a success rate of only 6%, while EPC60 excelled with a remarkable 100% success rate. Additionally, EPC60 successfully solved two 3-colorable graphs with 1,500 and 2,000 vertices, which had eluded Gurobi’s attempts for 15 days on a standard workstation. Given the mutual reducibility of NP-complete problems in polynomial time theoretically, the EPC stands out as a universal solver for NP-complete problem. The EPC can be applied to various problems that can be abstracted as combinatorial optimization issues, making it relevant across multiple domains, including supply chain management, financial services, telecommunications, energy systems, manufacturing, and beyond.