Solving 3-SAT and 3-dimensional matching in polynomial time

TL;DR

This paper proposes a novel approach using flow networks and minimum-cost flow algorithms to solve 3-SAT and 3-dimensional matching problems efficiently in polynomial time.

Contribution

It introduces a method that leverages conservative logic gates on flow networks to address NP-complete problems in polynomial time, challenging existing complexity assumptions.

Findings

3-SAT and 3D matching can be solved in polynomial time using flow network techniques.

The approach simplifies complex NP problems into flow network problems.

Potential implications for computational complexity theory.

Abstract

We show how the implementation of conservative logic gates on flow networks suggests a way to solve 3SAT and 3-dimensional matching problems in polynomial time by using standard minimum-cost flow methods.