A Comparison of Approaches for Solving Hard Graph-Theoretic Problems

TL;DR

This paper compares different computational approaches—parallel computing, quantum annealing, and SMT—for solving NP-hard graph problems, highlighting their formulation challenges and effectiveness.

Contribution

It introduces and evaluates multiple novel methods for tackling NP-hard graph problems, including quantum and SMT-based approaches.

Findings

Quantum annealing shows promise for certain instances.

SMT methods provide alternative formulations.

Parallel computing offers scalable solutions.

Abstract

In order to formulate mathematical conjectures likely to be true, a number of base cases must be determined. However, many combinatorial problems are NP-hard and the computational complexity makes this research approach difficult using a standard brute force approach on a typical computer. One sample problem explored is that of finding a minimum identifying code. To work around the computational issues, a variety of methods are explored and consist of a parallel computing approach using Matlab, a quantum annealing approach using the D-Wave computer, and lastly using satisfiability modulo theory (SMT) and corresponding SMT solvers. Each of these methods requires the problem to be formulated in a unique manner. In this paper, we address the challenges of computing solutions to this NP-hard problem with respect to each of these methods.