arXiv subjects

Mark Goh

Publications and source records attributed to Mark Goh.

5 recordsLinked to original sources

arXiv2026

Beyond Quantum Advantage: Improved Classical Algorithms for the Binary Paint Shop Problem

The binary paint shop problem (BPSP) is an APX-hard optimization problem in which, given $n$ car models that occur twice in a sequence of length $2n$, the objective is to find a colouring sequence such that each car model pair is painted differently while minimizing the number of times the paint is swapped along the sequence. A recent classical heuristic, known as the recursive star greedy (RSG) algorithm, is conjectured to achieve an expected paint swap ratio of $0.361$, thereby outperforming the Quantum Approximate Optimization Algorithm (QAOA) with circuit depth $p=7$. Since the performance of the QAOA with logarithmic circuit depth is instance independent, the average paint swap-ratio is upper-bounded by the QAOA. We provide an improved upper-bound of the BPSP by extending the QAOA to depth $p=17$, outputting an expected paint swap ratio of $0.334$ via an exact computation while numerical extrapolation suggests a further reduction to a value of $0.295$. To provide hardware-relevant comparisons, we additionally implement the BPSP on a D-Wave Quantum Annealer Advantage 2, obtaining a minimum paint swap ratio of $0.329$. Given that the QAOA with logarithmic circuit depth does not exhibit a quantum advantage for sparse optimization problems such as the BPSP, this implies the existence of a classical algorithm that outperforms both the RSG algorithm and logarithmic depth QAOA. We provide numerical evidence that the Mean-Field Approximate Optimization Algorithm (MF-AOA) is one such algorithm, yielding a paint swap ratio of approximately $0.280$ beating all known classical and quantum algorithms for the BPSP.

quant-ph↗

arXiv2024

Maritime Cybersecurity: A Comprehensive Review

The maritime industry stands at a critical juncture, where the imperative for technological advancement intersects with the pressing need for robust cybersecurity measures. Maritime cybersecurity refers to the protection of computer systems and digital assests within the maritime industry, as well as the broader network of interconnected components that make up the maritime ecosystem. In this survey, we aim to identify the significant domains of maritime cybersecurity and measure their effectiveness. We have provided an in-depth analysis of threats in key maritime systems, including AIS, GNSS, ECDIS, VDR, RADAR, VSAT, and GMDSS, while exploring real-world cyber incidents that have impacted the sector. A multi-dimensional taxonomy of maritime cyber attacks is presented, offering insights into threat actors, motivations, and impacts. We have also evaluated various security solutions, from integrated solutions to component specific solutions. Finally, we have shared open challenges and future solutions. In the supplementary section, we have presented definitions and vulnerabilities of vessel components that have discussed in this survey. By addressing all these critical issues with key interconnected aspects, this review aims to foster a more resilient maritime ecosystem.

cs.CR↗

arXiv2024

The Overlap Gap Property limits limit swapping in the QAOA

The Quantum Approximate Optimization Algorithm (QAOA) is a quantum algorithm designed for Combinatorial Optimization Problem (COP). We show that if a local algorithm is limited in performance at logarithmic depth for a spin glass type COP with an underlying Erd\"os--R\'enyi hypergraph, then a random regular hypergraph is similarly limited in performance as well. As such, we re-derived the fact that the average-case value obtained by the QAOA for even $q\ge 4$, Max-$q$-XORSAT is bounded away from optimality when optimised using asymptotic analysis due to the Overlap Gap Property (OGP). While this result was proven before, the proof is rather technical compared to ours. In addition, we show that the earlier result implicitly also implies limitation at logarithmic depth $p \le \epsilon \log n$ providing an improvement over limitation at constant depth. Furthermore, the extension to logarithmic depth leads to a tightening of the upper bound that the QAOA outputs at logarithmic depth for MaxCUT and Max-$q$-XORSAT problems. We also provide some numerical evidence the limitation should be extended to odd $q$ by showing that the OGP exists for the Max-$3$-XORSAT on random regular graphs.

quant-ph↗

arXiv2022

Guidelines for cyber risk management in shipboard operational technology systems

Over the past few years, we have seen several cyber incidents being reported, where some of the primary causes were the lack of proper security controls onboard the ship and crew awareness on cybersecurity. In response to the growing cyber threat landscape in the maritime sector, we have developed a set of guidelines for maritime cyber risk management, focusing on four major shipboard Operational Technology (OT) systems that are crucial for the day-to-day operation of ships. These four OT systems are: Communication Systems, Propulsion, Machinery and Power Control Systems, Navigation Systems and Cargo Management Systems. The guidelines identify the cyber risks in each of the OT systems and recommend the necessary actions that can be taken to manage risks in each shipboard OT system. In this paper, we introduce the new guidelines, which include cyber risks, mitigation measures, cyber risk assessment, and a checklist to help shipowners and maritime authorities assess and enhance cyber hygiene of their vessels. Our guidelines have been disseminated by the Maritime and Port Authority of Singapore (MPA) to owners and operators of the Singapore Registry of Ships for their reference and use.

cs.CR↗

arXiv2021

Generalized fractional grey system models: Memory effects perspective

As an essential characteristics of fractional calculus, the memory effect is served as one of key factors to deal with diverse practical issues, thus has been received extensive attention since it was born. By combining the fractional derivative with memory effects and grey modeling theory, this paper aims to construct an unified framework for the commonly-used fractional grey models already in place. In particular, by taking different kernel and normalization functions, this framework can deduce some other new fractional grey models. To further improve the prediction performance, the four popular intelligent algorithms are employed to determine the emerging coefficients for the UFGM(1,1) model. Two published cases are then utilized to verify the validity of the UFGM(1,1) model and explore the effects of fractional accumulation order and initial value on the prediction accuracy, respectively. Finally, this model is also applied to dealing with two real examples so as to further explain its efficacy and equally show how to use the unified framework in practical applications.

math.OC↗