Non-deterministic Polynomial-time Research Articles

Efficient Approaches to Solving Quadratic Diophantine Equations and their Time Complexity

In this paper, we present an efficient approach to solving quadratic Diophantine equations and analyze their time complexity. We propose a deterministic polynomial-time algorithm that provides an upper bound on the elementary operations required to solve such equations. We also present a non-deterministic polynomial-time algorithm for the construction of quadratic non-resiude modulo d, which is a more efficient alternative to the deterministic approach.

An enhanced multilevel secure data dissemination approximate solution for future networks.

Sensitive data, such as financial, personal, or classified governmental information, must be protected throughout its cycle. This paper studies the problem of safeguarding transmitted data based on data categorization techniques. This research aims to use a novel routine as a new meta-heuristic to enhance a novel data categorization based-traffic classification technique where private data is classified into multiple confidential levels. As a result, two packets belonging to the same confidentiality level cannot be transmitted through two routers simultaneously, ensuring a high data protection level. Such a problem is determined by a non-deterministic polynomial-time hardness (NP-hard) problem; therefore, a scheduling algorithm is applied to minimize the total transmission time over the two considered routers. To measure the proposed scheme's performance, two types of distribution, uniform and binomial distributions used to generate packets transmission time datasets. The experimental result shows that the most efficient algorithm is the Best-Random Algorithm ([Formula: see text]), recording 0.028 s with an average gap of less than 0.001 in 95.1% of cases compared to all proposed algorithms. In addition, [Formula: see text] is compared to the best-proposed algorithm in the literature which is the Modified decreasing Estimated-Transmission Time algorithm (MDETA). The results show that [Formula: see text] is the best one in 100% of cases where MDETA reaches the best results in only 48%.

An Efficient and Autonomous Planning Scheme for Deploying IoT Services in Fog Computing: A Metaheuristic-Based Approach

The fog computing paradigm is a promising concept to overcome the exponential increase in data volume in Internet of Things (IoT) applications. This paradigm can support delay-sensitive IoT applications by extending cloud services to the network edge. However, fog computing faces challenges such as resource allocation for applications at the network edge due to limited resources as well as its heterogeneous and distributed nature. This is in line with the goals of microservice architecture and develops the placement of microservice-based IoT applications. The IoT service placement problem (SPP) on fog nodes is known as non-deterministic polynomial-time (NP)-hard. In this study, we introduce a meta-heuristic approach named SPP-differential evolution algorithm (DEA) to handle SPP, which originates from the DEA with a shared parallel architecture. The proposed method takes advantage of the scalable and deployable nature of microservices to minimize the resource utilization and delay as much as possible. SPP-DEA is developed based on monitoring, analysis, decision-making, and execution with knowledge bas (MADE-k) autonomous planning model with the aim of compromise between service cost, response time, resource utilization, and throughput. In order to address the computational complexity of the problem, we consider the resource consumption distribution and service deployment priority in the placement process. In order to evaluate the quality of placement in SPP-DEA, extensive experiments have been performed on a synthetic fog environment. The simulation results show that compared to the state-of-the-art approaches, SPP-DEA reduces the service cost and waiting time by 16% and 11%, respectively.

Quality of services in software defined networking: challenges and controller placement problems

<span>Quality of service (QoS) is pivotal for ensuring effective and reliable network performance, yet achieving end-to-end QoS within current network architectures remains a persistent challenge. The emergence of software defined networking (SDN) addresses limitations in traditional networking by offering a centralized control plane. This allows dynamic resource management and efficient enforcement of QoS policies by network administrators. However, the controller placement problem (CPP) within SDN poses a significant challenge, as identifying the optimal placement of controllers is a non-deterministic polynomial-time hardness (NP-hard) problem. Researchers are actively working on solutions to address this challenge, especially in large-scale networks where deploying controllers becomes complex. Additionally, maintaining QoS in terms of controller management presents another hurdle. This paper explores these challenges, delving into the literature and providing a comprehensive analysis of controller performance metrics related to QoS parameters such as load balancing, reliability, consistency, and scalability. By addressing these challenges, the research aims to enhance QoS within the SDN framework.</span>

Quantum computing dataset of maximum independent set problem on king lattice of over hundred Rydberg atoms

Finding the maximum independent set (MIS) of a large-size graph is a nondeterministic polynomial-time (NP)-complete problem not efficiently solvable with classical computations. Here, we present a set of quantum adiabatic computing data of Rydberg-atom experiments performed to solve the MIS problem of up to 141 atoms randomly arranged on the king lattice. A total of 582,916 events of Rydberg-atom measurements are collected for experimental MIS solutions of 733,853 different graphs. We provide the raw image data along with the entire binary determinations of the measured many-body ground states and the classified graph data, to offer bench-mark testing and advanced data-driven analyses for validation of the performance and system improvements of the Rydberg-atom approach.

A relay-assisted parallel offloading strategy for multi-source tasks in internet of vehicles

Internet of Vehicles (IoV) is paving the road for the new generation of Intelligent Transportation Systems (ITS), and Mobile Edge Computing (MEC) is enabling IoV to efficiently handle the computation-intensive and time-sensitive tasks. However, this has introduced new challenges such as maximizing computing resources, allocating resources fairly for multi-source tasks concurrently, and dividing tasks for parallelly processing to minimize the latency. To face these challenges, a three-dimensional road vehicle mobility model is constructed, and the problem of offloading strategy and resource allocation among multiple vehicles served by one Road Side Unit (RSU) is investigates to minimize the average latency of multi-source tasks while satisfying the quality of service requirements. To address the Non-deterministic Polynomial-time hardness (NP-hardness) of the problem, we design a Relay-Assisted Parallel Offloading (RAPO) strategy to obtain the optimization solution. Extensive experimental results show that the RAPO strategy introducing relay-assisted nodes can enhance performance in poor scenarios and ensure low-latency multi-tasking under various conditions, especially reducing latency by 39% compared to local computing.

Optimization of transport constraints and quality of service for joint resolution of uncertain scheduling and the job-shop problem with routing (JSSPR) as opposed to the job-shop problem with transport (JSSPT)

To better meet the qualitative and quantitative requirements of customers or relevant sector managers, workshop environments are implementing increasingly complex task management systems. The job shop scheduling problem (JSSP) involves assigning each task to a single machine while scheduling many tasks on different machines. Finding the best scheduling for machines is one of the challenging optimizations of difficult non-deterministic polynomial (NP) time problems. The fundamental goal of optimization is to shorten the makespan (total execution time of all tasks). This paper is interested in the joint resolution of scheduling and transport problems and more particularly the Job-shop problem with Routing (JSSPR) as opposed to the Job-shop problem with Transport (JSSPT). These two problems are modeled in the form of a disjunctive graph. For the JSSPT, the solution to the transport problem is not linked to any quality of service (QoS) criterion and the solution is therefore often semi-active. The Job-shop with Routing explicitly considers transport operations and uses algorithms from the transport community to solve the transport problem. It is shown that the routing part of the JSSPR is a problem of the vehicle routing family and of the Pickup and Delivery Problem family. QoS in the JSSPR is defined by the duration of tours, the duration of transport of parts and the waiting time for them. A new evaluation function – named Time-Lag Insertion Heuristic (TLH) – is proposed to evaluate a disjunctive graph by simultaneously minimizing the makespan and maximizing the quality of service. Thus, the solution obtained is not semi-active, but a compromise between the different criteria. This evaluation function is included in a metaheuristic. Our numerical evaluations demonstrate that, on the one hand, the TLH evaluation can find almost optimal solutions regarding the QoS criterion; and on the other hand, the TLH evaluation is not very sensitive to the order of insertion of the maximum time-lags during the different minimization steps.

An optimization algorithm for maximum quasi-clique problem based on information feedback model.

The maximum clique problem in graph theory is a well-known challenge that involves identifying the complete subgraph with the highest number of nodes in a given graph, which is a problem that is hard for nondeterministic polynomial time (NP-hard problem). While finding the exact application of the maximum clique problem in the real world is difficult, the relaxed clique model quasi-clique has emerged and is widely applied in fields such as bioinformatics and social network analysis. This study focuses on the maximum quasi-clique problem and introduces two algorithms, NF1 and NR1. These algorithms make use of previous iteration information through an information feedback model, calculate the information feedback score using fitness weighting, and update individuals in the current iteration based on the benchmark algorithm and selected previous individuals. The experimental results from a significant number of composite and real-world graphs indicate that both algorithms outperform the original benchmark algorithm in dense instances, while also achieving comparable results in sparse instances.

Genetic PI Controller Tuning to Emulate a Pole Assignment Design

Tuning of proportional-integral (PI) and proportional-integral-derivative (PID) controllers continues to be a current topic, as the control needs in industry are broad and diverse. Although PID controllers have been the predominant controller type for several decades, there are still opportunities to improve the performance of both the installed base and newly deployed controllers. One of the main challenges is a reliable and easy tuning that can be performed by an operator on site. From a computer science point of view, the problem of tuning PID controllers qualifies as a nondeterministic polynomial-time hard problem (NP-hard). Genetic algorithms are a heuristic approach to approximate this type of problem, and the continued growth of computational capacity makes them increasingly more viable. In this work, we present a PID tuning architecture using a genetic algorithm, which incorporates in its fitness function an emulation of pole assignment and implicit cancellation of the additive dynamics of zeros in a closed loop, in addition to reducing discretization losses. The tuning is performed with a paradigm different from the one usually applied in the literature. Rather than simply minimizing the error between the process variable and the setpoint, the error between the process variable and an ideal response curve associated with a desired pole assignment is minimized. This approach provides better control over closed-loop performance.

Computation Offloading and Resource Allocation for E2E Tasks in Satellite Edge Computing Networks

Satellite edge computing shows promise in delivering seamless, low-latency services in challenging contexts such as deserts, oceans, and during natural disasters. Previous studies focused on the selection of suitable offloading nodes for task processing and result transmission to the original node. However, for end-to-end tasks, exemplified by applications like satellite-based remote sensing and forestry monitoring, the disparity between source and destination nodes emphasizes the importance of routing selection in data transmission. This aspect substantially limits the effectiveness of traditional computation offloading methods. In this paper, we formulate a joint computation offloading, routing, and multiple resource allocation optimization problem for end-to-end tasks in satellite edge computing networks. Moreover, to reduce the complexity of this nondeterministic polynomial-time hard (NP-hard) problem, we decompose it into the multidimensional resource allocation in fixed offloading and routing condition and the computation offloading and routing selection problem. An algorithm based on binary particle swarm optimization for joint computation offloading, routing, and multiple resource allocation optimization problem is proposed. Simulation results are presented to demonstrate the performance of our scheme compared with other baseline schemes.

A hybrid meta-heuristic algorithm for multi-objective IoT service placement in fog computing environments

The fog computing paradigm is promising for deploying various delay-sensitive Internet of Things (IoT) applications. The resource-constrained fog devices restrict the number of application deployments due to a lack of efficient resource estimation and discovery mechanisms for various emergent heterogeneous IoT applications. An efficient resource allocation strategy is one of the best choices to meet these application’s Quality of Service (QoS) requirements and improve system performance. However, finding the best allocation strategy for IoT applications with more than one QoS parameter is a challenge, and it has been proved as a non-deterministic polynomial time (NP)-complete problem. This article formulates a classical weighted multi-objective IoT service placement to optimize three parameters, i.e., makespan, cost, and energy. The non-convexity nature of the solution space motivates us to focus on the population-based meta-heuristic algorithm, i.e. Genetic Algorithm (GA), Simulated Annealing (SA) and Particle Swarm Optimization (PSO), along with their combination GA-SA, and GA-PSO. It implements the algorithm and compares it with the greedy-based random placement approach, varying the number of IoT applications with different parameters. The final results reveal that the hybrid method GA-SA outperforms other state-of-the-art algorithms.

Sustainable management of EOL tyres: A remanufacturing supply chain network design

End-of-life (EOL) objects such as tyres have been categorised as hazardous to the environment due to heavy metals and chemicals. To manage the recovery and remanufacturing operations of these EOL items, an effective network design is necessary. In this paper, we developed a mixed integer linear programming (MILP) model to minimize the total cost of the proposed EOL tyre remanufacturing supply chain network. Since, the problem is Non-deterministic Polynomial time hardness (NP-hard) in nature, we propose a prediction model that evaluates the operational feasibility of vehicle allocation and an evolutionary algorithm-based technique is employed to identify optimal facility locations, material flows among facilities, and demand distribution to individual automobiles for near-optimal solutions. Numerical experiments were conducted on a leading tyre remanufacturing company as a case study, and the results were compared with several evolutionary algorithms found that the Modified Genetic Algorithm (MGA) outperforms other algorithms. We demonstrate how, in each case, an optimal cost-effective location for a factory is found based on the cost and demand of the products. The study findings can assist governments and industry stakeholders in developing successful EOL tyre management strategies.

Routing and scheduling co-design for holistic software-defined deterministic network

As a result of the growing complexity of industrial Internet applications, traditional hardware-based network designs are encountering challenges in terms of programmability and dynamic adaptability as they struggle to meet the real-time, high-reliability transmission requirements for the vast quantities of data generated in industrial environments. This paper proposes a holistic software-defined deterministic network (HSDDN) design solution. This solution uses a centralized controller to implement a comprehensive software definition, ranging from the network layer down to the physical layer. Within the wireless access domain, we decouple the standard radio-frequency modules from baseband processing to realize a software-defined physical layer, which then allows us to adjust the data transmission cycles and tag the trigger rates to meet demand for low-power, high-concurrency transmission. Within the wired network domain, we integrate software-defined networking with time-sensitive networking and propose a coordinated design strategy to address routing and the deterministic scheduling problem. We define a set of constraints to ensure collaborative transmission of the periodic and aperiodic data flows. To guarantee load balancing across all paths and timeslots, we introduce the Jain’s fairness index as the optimization objective and then construct a nondeterministic polynomial-time (NP)-hard joint optimization problem. Furthermore, an algorithm called Tabu search for routing and scheduling with dual-stages (TSRS-DS) is proposed. Simulation experiments demonstrate the effectiveness of the proposed HSDDN architecture.

A Dynamically Programmable Quantum Photonic Microprocessor for Graph Computation

AbstractQuantum computing has grown extensively, especially in system design and development, and the current research focus has gradually evolved from validating quantum advantage to practical applications. In particular, nondeterministic‐polynomial‐time (NP)‐complete problems are central in numerous important application areas. Still, in practice, it is difficult to solved efficiently with conventional computers, limited by the exponential jump in hardness. Here, a quantum photonic microprocessor based on Gaussian boson sampling (GBS) that offers dynamic programmability to solve various graph‐related NP‐complete problems is demonstrated. The system with optical, electrical, and thermal packaging implements a GBS with 16 modes of single‐mode squeezed vacuum states, a universal programmable 16‐mode interferometer, and a single photon readout on all outputs with high accuracy, generality, and controllability. The developed system is applied to demonstrate applications in solving NP‐complete problems, manifesting the ability of photonic quantum computing to realize practical applications for conventionally intractable computations. The GBS‐based quantum photonic microprocessor is applied to solve task assignment, Boolean satisfiability, graph clique, max cut, and vertex cover. These demonstrations suggest an excellent benchmarking platform, paving the way toward large‐scale combinatorial optimization.

Iterative quantum algorithm for combinatorial optimization based on quantum gradient descent

Combinatorial optimization has wide and high-value applications in many fields of science and industry, but solving general combinatorial optimization problems is non-deterministic polynomial time (NP) hard. Many such problems can be mapped onto the ground-state-search problems of the Ising model. Here, an iterative quantum algorithm based on quantum gradient descent to solve combinatorial optimization problems is introduced, where the initial state of a quantum register evolves over several iterations to a good approximation of the Ising-Hamiltonian ground state. We verified the effectiveness of the proposed algorithm in solving the MaxCut problem for different types of undirected graphs by numerical simulations, and analyzed the robustness of the algorithm to errors by simulating random error and Gaussian error. We compared the performance of the algorithm with the quantum approximate optimization algorithm, and the results indicate that the proposed algorithm has comparable convergence performance. We also verified the feasibility of the algorithm by conducting experiments on a real quantum computer through the quantum cloud platform. Our work provides a potential method for solving combinatorial optimization problems on future quantum devices without the use of complex classical optimization loops.

An Underground Mine Safety-Oriented Optimization Model for Mine Tailings Backfill Scheduling Considering Multi-Process and Multi-Cycle Issues

The backfill mining method is adopted in many mines around the world because it can reliably handle underground mine tailings and eliminate dangers in goafs. It is necessary to improve backfilling resource allocation and efficiency, thereby eliminating safety hazards and providing reliable support for the next stage of mining as quickly as possible. In this paper, we propose a backfill-scheduling optimization model that considers multiple processes, resource constraints, and operating capabilities. The purpose of this model is to minimize the exposure time of goafs. This NP-hard (Nondeterministic Polynomial-time hard) problem has a non-inferior implemented solution through multiple iterations of genetic, crossover, and mutation operations of the genetic algorithm. The results show that the model significantly reduces the backfilling-delay time and backfilling-operation time.

The Maximum Clique Problem and Integer Programming Models, Their Modifications, Complexity and Implementation

The maximum clique problem is a problem that takes many forms in optimization and related graph theory problems, and also has many applications. Because of its NP-completeness (nondeterministic polynomial time), the question arises of its solvability for larger instances. Instead of the traditional approaches based on the use of approximate or stochastic heuristic methods, we focus here on the use of integer programming models in the GAMS (General Algebraic Modelling System) environment, which is based on exact methods and sophisticated deterministic heuristics incorporated in it. We propose modifications of integer models, derive their time complexities and show their direct use in GAMS. GAMS makes it possible to find optimal solutions to the maximum clique problem for instances with hundreds of vertices and thousands of edges within minutes at most. For extremely large instances, good approximations of the optimum are given in a reasonable amount of time. A great advantage of this approach over all the mentioned algorithms is that even if GAMS does not find the best known solution within the chosen time limit, it displays its value at the end of the calculation as a reachable bound.

CHR++: An efficient CHR system in C++ with don’t know non-determinism

This article introduces CHR++, an implementation of CHR (Constraint Handling Rules) in C++. CHR++ has been designed to be efficient, user-friendly, and to make it easier to model problems of NP (Non-deterministic Polynomial time) complexity class thanks to the support of don’t know non-determinism. CHR++ conforms to the refined semantics of CHR and provides a high-level syntax similar to the historical CHR implementations in Prolog. It is a powerful system that incorporates many of the high-level optimisations known to date. Like implementations made on top of Prolog, it handles don’t know non-determinism through support for the CHR extension. CHR++ is the first non-Prolog CHR system that natively supports don’t know non-determinism. It makes it easier to model constrained decision or optimisation problems and shows a significant gain in efficiency compared with CHR Prolog systems. It equals or exceeds the fastest CHR systems in Java and C, but is able to tackle a whole class of problems unattainable by those systems.

How to operate ship fleets under uncertainty

Ships operated by a liner company are scattered around the world to transport goods. A liner company needs to adjust its shipping network every few months by repositioning its ships to respond to uncertain container shipping demand. Few studies investigate a liner company's multiperiod heterogeneous fleet deployment problem under uncertainty, considering fleet repositioning, ship chartering, demand fulfillment, cargo allocation, and adaptive fleet sizes. To this end, this study formulates a mixed‐integer linear programming model that captures all of these elements. This study also designs a Benders‐based branch‐and‐cut algorithm for this non‐deterministic polynomial‐time (NP)‐hard problem. Two types of acceleration strategies, including approximate upper bound tightening inequalities and Pareto‐optimal cuts, are applied to improve the performance of the algorithm. Extensive numerical experiments show that the proposed algorithm significantly outperforms CPLEX and its Benders decomposition framework in solving the model. We conduct an intensive analysis and find that multistage stochastic programming can lead to better solutions than two‐stage stochastic programming. We also find that 10% of the benefit provided by the multistage model over the two‐stage model is due to better fleet deployment decisions and that 90% of the benefit is due to better demand fulfillment and allocation decisions. By exploring three practical questions regarding driver analysis of liner company profitability, benefits analysis of adaptive fleet sizes, and the influence of the COVID‐19 pandemic on liner shipping, we show how liner companies can benefit from managerial insights obtained in this study.

IoT-based milk-run routing for manufacturing system: an application case in an automotive company

The Internet of Things (IoT) provides new opportunities to improve manufacturing lines’ performance and in-plant logistic processes. The digital milk-run system represents the new frontier to optimize material handling strategies but is still not fully exploited to address material distribution depending on the time slots required by the manufacturing lines. Therefore, to fill this gap, this paper investigates the actual integration of the milk-run system with an IoT system. An analytical model for planning a dynamic routing strategy for tugger trains to deliver the materials to different workstations of a production line has been developed. The proposed model provides a materials distribution consistent with the time slot required by the manufacturing line, ensuring the minimisation of the total distance of the routes. An algorithm developed in Python is proposed to solve the NP-hard problem (nondeterministic polynomial time problem). The model has been applied to a real case of a worldwide automotive company to validate and prove its efficacy and efficiency. Indeed, compared to the current in-plant logistic strategy, (i) the inventory stock of each workstation was ensured, (ii) the average utilization rate of the tugger trains’ fleet was improved, and (iii) the daily path was minimized.