NP-complete Research Articles

An efficient algorithm for maximum cliques problem on IoT devices

This work describes how the maximum clique problem (MCP) algorithm can be performed on microcontrollers in a dynamic environment. In practice, many problems can be formalised using MCP and graphs where our problem is considered in the context of a dynamic environment. MCP is, however, a tricky problem NP-Complete for which suitable solutions must be designed for microcontrollers. Microcontrollers are built for specific purposes and optimised to meet different constraints, such as timing, nested recursion depth limitation, or no recursion at all due to recursion stack limitation, power, and RAM limitation. On another side, graph representation and all the algorithms mentioned in the literature to solve the MCP problem, which is recursive, consumes memory and is designed specifically for computers rather than a microcontroller.

Multi-objective steel plate cutting optimization problem based on real number coding genetic algorithm

The rectangular packing problem is an NP-complete combinatorial optimization problem. This problem occurs widely in social production scenarios, with steel plate cutting being one example. The cutting scheme for the rectangular packing problem needs to be improved because, without the globally optimal solution, there are many unnecessary edges in the steel cutting process. Based on a practical roll-fed disc shearing steel plate optimization problem, this paper explores a generalized packing method for rectangles of special dimensions and abstractly condenses complex quantitative relationships to establish a multi-objective mixed-integer nonlinear programming model. An innovative algorithm design based on a genetic algorithm is established to plan the cutting scheme in a high-speed and efficient way. The outcome is a utilization rate of up to 92.73% for raw materials and a significant reduction in labor, providing a guide for practical production and processing tasks. The advantages and disadvantages of the model and algorithm are discussed, and it is concluded that this rectangular packing method has strong universality and generalization ability, allowing rectangular packing tasks with large data volumes to be completed within a short time.

On Finding Hamiltonian Cycles in Barnette Graphs

In this paper we deal with hamiltonicity in planar cubic graphs G having a facial 2–factor 𝒬 via (quasi) spanning trees of faces in G/𝒬 and study the algorithmic complexity of finding such (quasi) spanning trees of faces. Moreover, we show that if Barnette’s Conjecture is false, then hamiltonicity in 3–connected planar cubic bipartite graphs is an NP-complete problem.

A Multi Objective Hybrid Collision-free Optimal Path Finder for Autonomous Robots in Known Static Environments

The most important field of robotics study is path planning. Path planning problem in general is an NP-complete problem. Though several attempts have been made using A*, PRM, RRT, and RRT* these algorithms explore too many nodes in the state space, not completely captured kinematic constraints, and are not optimal in real-time. In this paper, a Multi-Objective Hybrid Collision- free Optimal Path Finder (MOHC-OPF) is proposed which is an attempt to obtain a near-optimal solution by exploring fewer nodes compare to the above existing methods while considering kinematic constraints aiming to generate optimal drivable paths. The empirical study revealed that the proposed algorithm is capable of detecting static obstacles and finding a collision-free nearest-optimal, smooth and safe path to the destination in a static known environment. Multiple criteria, including path length, collision-free, execution time, and smooth path, are used to determine an optimal path.. The proposed algorithm shows efficiency in finding the shortest path length and execution time decreased in 90% of the experiments.

Heuristic smoothing ant colony optimization with differential information for the traveling salesman problem

The traveling salesman problem (TSP) is an NP complete problem with potential applications. Thus far, numerous approaches have been proposed to solve the TSP including exact, heuristic and metaheuristic methods. Among them, the ant colony optimization (ACO) algorithm, belonging to metaheuristic methods, has proven to be an efficient method for solving the TSP. However, the phenomena of rapid convergence to local optima and unsatisfactory computational accuracy distinctly limit the performance of ACO. This study therefore proposes a novel ACO algorithm (HSDACO) to compensate for these shortcomings. In the HSDACO algorithm, the involvement of heterogeneous population automation at each iteration generates better candidate solutions with maintaining parameter diversity. Then, the implementation of three smoothing techniques with the 2-Opt method guarantees the effective assessment of candidate solutions in favor of higher quality. Next, the introduction of a differential information updating mechanism, using differential edge information obtained from the candidate solutions, enables the evaporation operation of the pheromone trail to obtain more reasonable guidance. Subsequently, the design of evolutionary state estimation and adjustment is used to monitor the population under correct guidance and regulate the evolutionary state effectively and efficiently. Finally, the HSDACO algorithm is evaluated on public TSP benchmark instances and compared with the other state-of-the-art algorithms. Experimental results show that the proposed HSDACO achieves substantial improvement for mid-scale TSP instances and overwhelming advantages for small-scale TSP instances, in terms of solution accuracy and convergence speed.

An intelligent energy efficient optimized approach to control the traffic flow in Software-Defined IoT networks

In modern society numerous digital devices play a very significant role in day-to-day life. Digital devices are well connected and easily accessible through multiple sensors and Internet of Things (IoT) devices. Due to the rapid growth of digital devices, large amount of data traffics are being generated, which induces network congestion. To deal with large amount of data traffic a programmable Software Defined IoT (SD-IoT) infrastructure is utilized. For efficient and sustainable network, the data must be transmitted through optimal path in such a way to as to minimize energy consumption. Here, the network is partitioned into clusters to find an optimal path. Finding an optimal path from a set of possible paths is an NP-complete problem. To solve this problem, we propose to find a set of optimal border nodes of each cluster with other clusters in the network, so as to reduce the number of possible paths between clusters. The set of optimal border nodes will be selected in such a way so that they have maximum energy and minimum distances. This paper proposes an intelligent approach to find the set of optimal border nodes using Lion Swarm Optimization algorithm (LSOA). Once a set of optimal border nodes are obtained, an optimal path can be generated using a routing mechanism. The performance of the proposed work is analyzed in terms of packet delivery ratio, average latency, network lifetime and energy consumptions. The results show that the border nodes selected using LSOA finds better routes as compared to the border nodes selected using other state-of-the-art metaheuristics algorithm thereby, increases suitability of the network by energy conservation.

Solving a Multi-Conveyance Travelling Salesman Problem using an Ant Colony Optimization Method

Objectives: A well-known NP-complete problem is the travelling salesman problem (TSP). It has numerous engineering and scientific applications. In this article, we have proposed a multi-conveyance TSP where different conveyances are present to travel from one city to another city. This is an extension to classical TSP. In this TSP, the salesman visits all the cities only once during his/her tour, using different conveyances to travel from one city to another. The cost of travelling between cities using various modes of conveyance varies. The objective of this research is to find the minimum cost tour using an ant colony optimization (ACO) based approach by satisfying the constraints of the proposed multi-conveyance TSP. Method: The considered TSP has been solved using a novel ACO technique. The proposed ACO is adopted with the Roulette-wheel selection and “tuning solution” techniques. We have used a few benchmark datasets from TSPLIB to check the effectiveness of the proposed algorithm. The experimental findings for a few benchmarks TSP instances show that almost always, the proposed ACO is able to find a better result. Then, we used some redefined and randomly generated datasets for experiments. The experimental outcomes for various input datasets are also very encouraging. Findings: The goal of the proposed TSP is to find a complete tour with a minimum cost without exceeding the total travel cost and total travel time. Thus, there are two novel constraints in the classical TSP. Novelty: A unique aspect of the proposed research is the use of several conveyance facilities and a fixed total travel time and cost. This is new, as these three factors are integrated into a single TSP model. Keywords: Travelling Salesman Problem; Travel Cost; Travel Time; MultiConveyance TSP; Ant Colony Optimization

Real-time Virtual Machine Energy-Efficient Allocation in Cloud Data Centers Using Interval-packing Methods

The reduction of power consumption, which can lower the operation costs of Cloud providers, lengthen the useful life of a machine, as well as lessen the environmental effect caused by power consumption, is one of the critical concerns for large-scale Cloud applications. To satisfy the needs of various clients, Virtual Machines (VMs) as resources (Infrastructure as a Service (IaaS)) can be dynamically allocated in cloud data centers. In this research, we study the energy-efficient scheduling of real-time VMs by taking set processing intervals into account, with the providers' goal of lowering power consumption. Finding the best solutions is an NP-complete problem when virtual machines (VMs) share arbitrary amounts of a physical machine's (PM) total capacity, as demonstrated in numerous open-source resources. Our strategy treats the issue as a modified interval partitioning problem and takes into account configurations with dividable capacities to make the problem formulation easier and assist save energy. There are presented both exact and approximate solutions. The proposed systems consume 8–30% less power than the existing algorithms, according to simulation data.

Identification Conditions for the Solvability of NP-Complete Problems for the Class of Prefractal Graphs

Modern network systems (unmanned aerial vehicles groups, social networks, network production chains, transport and logistics networks, communication networks, and cryptocurrency networks) are distinguished by their multielement nature and the dynamics of connections between their elements. A number of discrete problems on the construction of optimal substructures of network systems described in the form of various classes of graphs are NP-complete problems. In this case, the variability and dynamism of the structures of network systems lead to an additional complication of the search for solutions to discrete optimization problems. At the same time, for some subclasses of dynamic graphs that are used to model the structures of network system, conditions for the solvability of a number of NP-complete problems can be distinguished. This subclass of dynamic graphs includes prefractal graphs. This article investigates NP-complete problems on prefractal graphs: a Hamiltonian cycle, a skeleton with the maximum number of pendant vertices, a monochromatic triangle, a clique, and an independent set. The conditions under which it is possible to obtain an answer about the existence of and construct polynomial (when fixing the number of seed vertices) algorithms for finding solutions for some problems are identified.

Method of cutting metal ingot with changing direction of deformation

The paper considers the priority problem of cutting an ingot with a changing direction of rolling which can be presented as a priority problem of packaging with incompatible categories and dynamically changing bin sizes. This problem is a NP-complete optimization problem which is often found in the production of metalwork. Priorities reflect the “importance” of manufacturing elements for production and incompatible categories show that elements of different thicknesses cannot be made from the same bin. In addition, we use guillotine restrictions to take into account the specifics of production. The problem of cutting the ingot is characterized by the fact that the bin sizes are not known in advance. Thus, the task is to find the optimal bin sizes, the sequence of actions and the placement of elements in these bins. We propose a sequential tree metaheuristic to solve this problem. It is a deterministic method. This method is based on sequential metaheuristic which was proposed by the authors earlier. The proposed method also has the ideas of dividing a set of elements into groups and subgroups by thickness and priorities, as well as their sequential packing. However, it differs from previous one in that it uses a tree to represent options for rolling operations. The best subtree from the point of view of any criterion, formed as a path from the root to one of the nodes, will be the solution. The ability to find several better solutions with the same value of the criterion is another advantage of the proposed method. Such a situation may arise, for example, for a square ingot. In this case, two solutions are possible with accuracy up to 90 degrees rotation of the workpieces. The priority heuristic is used as a heuristic to solve the packaging subproblem. The results of computational experiments are based on test cases which were compiled specially. Test instances differ in the number and characteristics of elements, categories, priorities. The results show that the metaheuristic proposed by the authors solves the problem effectively.

Efficient Flow-Based Scheduling for Geo-Distributed Simulation Tasks in Collaborative Edge and Cloud Environments

Edge computing is a good complement to cloud computing for deploying large-scale geo-distributed simulation applications, which are very sensitive to the communication delay among different simulation components (also called tasks in this paper) and users. We mainly focus on the efficient scheduling of simulation components in collaborative edge and cloud environments. As components should be deployed jointly with the consideration of capacity constraints of hosts, it is actually an NP-complete multi-dimensional bin packing problem. Meanwhile, dynamic changes of component and host states require the low deployment latency of scheduling algorithms. Unfortunately, most of the existing schedulers for modern clusters are queue-based, in which tasks are scheduled sequentially, thus lacking the ability to process tightly coupled tasks jointly. Other batching-based placement algorithms are usually time-consuming. This paper describes Pond, a novel flow-based scheduler with the awareness of interactions among tasks and users as well as heterogeneous multi-dimensional resources. First, characteristics of distributed simulation tasks are analysed and the scheduling problem is formulated as a min-cost max-flow (MCMF) problem over the flow network by mapping the communication overhead among tasks and users to the costs of arcs in the network. Considering the inherent defects of existing flow-based schedulers in dealing with multi-dimensional resources, a new method based on dominant resource is proposed and some problem specific heuristics are also designed. Extensive simulation experiments based on Alibaba production trace and some random synthetic parameters are conducted. Results show that Pond can reduce the average communication cost for each task significantly in a quite low deployment latency compared with some baselines.

Optimisation of robotic disassembly plans using the Bees Algorithm

Remanufacturing is a key component of a circular economy. It enables the reduction of landfill and the preservation of natural resources, therefore benefiting the environment. Disassembly is the first stage in the remanufacturing process, but, so far, has been mostly a manual operation. Transitioning from manual to robotic disassembly is desirable in the Industry 4.0 era. A model for planning the sequence of steps a robot needs to take to dismantle a product is proposed in this study. The model has three objectives: to maximise profits, energy savings and reduction in greenhouse gas emissions. The Bees Algorithm, an algorithm inspired by the foraging behaviour of honey bees, was used to obtain near-optimal plans for disassembling gear pumps. Statistical tests were performed on the results obtained with different optimisation parameters to establish statistical significance. They show that the Bees Algorithm was able to optimise disassembly plans for profits, energy savings and reductions in greenhouse gas emissions. • Optimisation of robotic disassembly plans to maximise profits, energy savings and reduction in greenhouse gas emissions. • Application of the Bees Algorithm to an NP-complete optimisation problem. • Bibliometric literature review of robotic disassembly revealings that the field is understudied.

A Deep Reinforcement Learning-Based QoS Routing Protocol Exploiting Cross-Layer Design in Cognitive Radio Mobile Ad Hoc Networks

In this paper, we propose a novel deep reinforcement learning-based quality-of-service (QoS) routing protocol, namely DRQR, exploiting cross-layer design to establish efficient QoS (EQS) routes in cognitive radio mobile ad hoc networks. An EQS route is a route with minimum end-to-end (E2E) queuing delay subject to QoS constraints such as link stability, residual energy, number of hops and avoiding licensed channels of primary users. Particularly, we propose an NP-complete optimization problem which has a feasible solution as an EQS route. To tackle this problem, we design a new deep reinforcement learning model which supports the DRQR protocol to establish EQS routes in real time by offline training instead of online training like most of literature studies. Moreover, the DRQR protocol guarantees to have high system performance. A mathematical analysis of the E2E queuing delay with random waypoint mobility model also provides to verify simulation results. Numerical results show that the DRQR protocol outperforms state-of-the-art routing protocols in terms of routing delay, queuing delay, control overhead, PDR and energy consumption.

ОПРЕДЕЛЕНИЕ НЕЧЕТКИХ УСЛОВИЙ И АНАЛИЗ СУЩЕСТВУЮЩИХ РЕШЕНИЙ В ЗАДАЧЕ ЭВАКУАЦИИ ПРИ ЧРЕЗВЫЧАЙНЫХ СИТУАЦИЯХ

Quantification in collective behavior and decision-making in fuzzy conditions is crucial toensure the health and safety of the population. The task of modeling and predicting behavior infuzzy conditions, as is known, has increased complexity due to a large number of factors fromwhich an NP-complete multi-criteria problem is formed. There is a difficulty in quantifying the impact of fuzzy factors using a mathematical model. In this regard, the paper proposes a stochasticmodel of human decision-making to describe the empirical behavior of subjects in an experimentsimulating an emergency scenario. The developed fuzzy model combines fuzzy logic into aconventional model of social behavior. Unlike existing models and applications, this approachuses fuzzy sets and membership functions to describe the evacuation process in an emergencysituation. The purpose of this work is to define fuzzy rules and analyze existing solutions. The scientificnovelty lies in the formation of a set of factors that form fuzzy rules for making dynamicdecisions. The problem statement in this paper is as follows: to form a set of factors affecting thebehavior of pedestrians, which are modeled as fuzzy input data. The practical value of the worklies in the creation of a new set of fuzzy rules that allows them to be used in the evacuation algorithmfor the effective solution of the task. The fundamental difference from the known approachesis in the application of a new set of fuzzy rules, which contains factors: perception, intention, attitude.To implement the proposed model, the process of social behavior during evacuation, independentvariables are determined. These variables include measurements related to social factors,in other words, the behavior of individual subjects and individual small groups, which are fundamentalat an early stage of evacuation.

Revising Johnson’s table for the 21st century

What does it mean today to study a problem from a computational point of view? We focus on parameterized complexity and on Column 16 “Graph Restrictions and Their Effect” of D.S. Johnson’s Ongoing guide, where several puzzles were proposed in a summary table with 30 graph classes as rows and 11 problems as columns. Several of the 330 entries remain unclassified into Polynomial or NP-complete after 35 years. We provide a full dichotomy for the Steiner Tree column by proving that the problem is NP-complete when restricted to Undirected Path graphs. We revise Johnson’s summary table according to the granularity provided by the parameterized complexity for NP-complete problems.

A New Approach Based on Centrality Value in Solving the Minimum Vertex Cover Problem: Malatya Centrality Algorithm

The graph is a data structures and models that used to describe many real-world problems. Many engineering problems, such as safety and transportation, have a graph-like structure and are based on a similar model. Therefore, these problems can be solved using similar methods to the graph data model. Vertex cover problem that is used in modeling many problems is one of the important NP-complete problems in graph theory. Vertex-cover realization by using minimum number of vertex is called Minimum Vertex Cover Problem (MVCP). Since MVCP is an optimization problem, many algorithms and approaches have been proposed to solve this problem. In this article, Malatya algorithm, which offers an effective solution for the vertex-cover problem, is proposed. Malatya algorithm offers a polynomial approach to the vertex cover problem. In the proposed approach, MVCP consists of two steps, calculating the Malatya centrality value and selecting the covering nodes. In the first step, Malatya centrality values are calculated for the nodes in the graph. These values are calculated using Malatya algorithm. Malatya centrality value of each node in the graph consists of the sum of the ratios of the degree of the node to the degrees of the adjacent nodes. The second step is a node selection problem for the vertex cover. The node with the maximum Malatya centrality value is selected from the nodes in the graph and added to the solution set. Then this node and its coincident edges are removed from the graph. Malatya centrality values are calculated again for the new graph, and the node with the maximum Malatya centrality value is selected from these values, and the coincident edges to this node are removed from the graph. This process is continued until all the edges in the graph are covered. It is shown on the sample graph that the proposed Malatya algorithm provides an effective solution for MVCP. Successful test results and analyzes show the effectiveness of Malatya algorithm.

Generalized binary utility functions and fair allocations

The problem of finding envy-free allocations of indivisible goods cannot always be solved; therefore, it is common to study some relaxations such as envy-free up to one good (EF1) and envy-free up to any positively valued good (EFX). Another property of interest for the efficiency of an allocation is the Pareto Optimality (PO). Under additive utility functions for goods, it is possible to find EF1 and PO allocations using the Nash social welfare. However, finding an allocation that maximizes the Nash social welfare is a computationally costly problem. Maximizing the utilitarian social welfare subject to EF1 constraints is an NP-complete problem for the case where three or more agents participate. In this work, we propose a restricted case of additive utility functions called generalized binary utility functions. The proposed utilities are a generalization of binary and identical utilities simultaneously. In this scenario, we present a polynomial-time algorithm that maximizes the utilitarian social welfare and, at the same time, produces an EF1 and PO allocation for goods as well as for chores. Moreover, a slight modification of our algorithm gives a better allocation: one which is EFX.

Integer Factorization: Why Two-Item Joint Replenishment Is Hard

Joint replenishment problems constitute an important class of models in inventory management. They exhibit aspects of possible coordination among multiple products to save costs. Their computational complexity had been open even if there are just two products that need to be synced. In “Integer factorization: Why two-item joint replenishment is hard,” Schulz and Telha present a simple framework based on integer factorization to establish the computational hardness of two variants of the joint replenishment problem with two items. Whereas difficult to solve in practice and not believed to be solvable in polynomial time, integer factorization is not as difficult as NP-complete problems. The authors show that a similar technique can be used to show even the NP-completeness of one variant of the joint replenishment problem (again with just two items).

An enhanced approach for solving winner determination problem in reverse combinatorial auctions

<span>When a disaster occurs, the single agent does not have complete knowledge about the circumstances of the disaster. Therefore, the rescue agents should coordinate with each other to perform their allocated tasks efficiently. However, the task allocation process among rescue agents is a complex problem, which is NP-complete problem, and determining the rescue agents that will perform the tasks efficiently is the main problem, which is called the winner determination problem (WDP). This paper proposed an enhanced approach to improve rescue agents’ tasks allocation processes for WDP in reverse combinatorial auctions. The main objective of the proposed approach is to determine the winning bids that will perform the corresponding tasks with minimum cost. The task allocation problem in this paper was transformed into a two-dimensional array, and then the proposed approach was applied to it. The main contribution of the proposed approach is to shorten the search space size to determine the winners and allocate the corresponding tasks for a combination of agents (i.e., more than two agents). The proposed approach was compared to the genetic algorithm regarding the execution time, and the results showed good performance and effectiveness of the proposed approach.</span>

Correlating the Community Structure of Constraint Satisfaction Problems with Search Time

A constraint satisfaction problem (CSP) is, in its most general form, an NP-complete problem. One of the several classes of tractable problems that exist contains all the problems with a restricted structure of the constraint scopes. This paper studies community structure, a particular type of restricted structure underpinning a class of tractable SAT problems with potentially similar relevance to CSPs. Using the modularity, it explores the community structure of a wide variety of problems with both academic and industrial relevance. Its impact on the search times of several general solvers, as well as one that uses tree-decomposition, is also analysed to determine whether constraint solvers exploit this type of structure. Nearly all CSP instances have a strong community structure, and those belonging to the same class have comparable modularity values. For the general solvers, strong correlations between the community structure and the search times are not apparent. A more definite correlation exists between the modularity and the search times of the tree-decomposition, suggesting that it might, in part, be able to take advantage of the community structure. However, combined with the relatively strong correlation between the modularity and the tree-width, it could also indicate a similarity between these two measures.