A comparison of approaches for finding minimum identifying codes on graphs

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, an adiabatic quantum optimization approach using a D-Wave quantum annealing processor, 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.

A Population-Based Local Search Algorithm for the Identifying Code Problem

“…In [18], Xiao et al formulated the problem using an integer program and developed a genetic algorithm to solve it. Recently, Horan et al [19] compared three approaches for finding minimum identifying codes on Brujin graphs using quantum annealing.…”

Mathematical Methods for a Quantum Annealing Computer

“…The design and fabrication of several generations of quantum annealing computers (QACs) to solve hard optimization problems has aroused interest in their expected speedup [8,14,26], real-world applications [1,2,4,9,21,22,25], and benchmarks [14 -16]. Current research is focused on framing old problems to quantum annealing [10,18,30], embedding problems into quantum bits and their connections [5,13], suppressing errors due to the nature of the apparatus [11,21,24], scaling large data to fit QACs [23], and comparing quantum annealers with thermal annealers [19,21]. The above list of topics and [32] indicate that we are working in an interdisciplinary field.…”