NP Problem Research Articles

A Theory of NP-completeness and Ill-conditioning for Approximate Real Computations

We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The theory admits deterministic and nondeterministic polynomial time recognizable problems. We prove that P is not NP in this theory if and only if P is not NP in the BSS theory over the reals. Then we develop a theory with weak and strong approximate computations. This theory is intended to model actual numerical computations that are usually performed in floating point arithmetic. It admits classes P and NP and also an NP-complete problem. We relate the P vs. NP question in this new theory to the classical P vs. NP problem.

Comparison of CPG\u2019s for the diagnosis, prognosis and management of non-specific neck pain: a systematic review

BackgroundNeck pain (NP) is a very common musculoskeletal condition with potential for a high burden in disability and length of disorder. Clinical practice guidelines (CPG) give recommendations to clinicians for providing optimal care for patients however best practice recommendations are often contradictory. The purpose for this review was to conduct a SR of CPGs to assess the management recommendations for NP (diagnosis, treatment, prognosis, imaging).MethodsStandard SR methodology was employed including a grey literature search (including the National Guideline Clearing House). Medline, Cinahl, Embase, ILC, Cochrane, Central, and Lilacs were searched from 1995-to March 2018. Two raters evaluated all citations and a third rater resolved any disagreements. The AGREE II was used to assess risk of bias of each CPG. Data was extracted and included CPG purpose, type of NP problem and clinical recommendations. The AGREE II critical appraisal tool was used to assess risk of bias of each CPG.ResultsFrom 640 articles, 241 were available for screening. A total of 46 guidelines were selected. CPG’s were categorized by the NP population (General NP, whiplash, interventional, headache and risk for vertebral insufficiency) and type of clinical aim (diagnosis, prognosis, treatment, imaging). Each clinical NP population had a large overlap of clinical aims presented. The CPGs were directed to a variety of clinicians that included physicians, physiotherapists and chiropractors. Results suggest heterogeneity in CPG recommendations within each clinical aim. CPG characteristics accounting for these differences are outlined.ConclusionThe majority of CPGs were developed for general NP that focused on treatment recommendations, with fewer number aimed at recommendations for diagnosis, prognosis, and outcomes. Heterogeneity of recommendations within the categories were noted as were potential factors associated with these differences, including CPG quality as assessed by the AGREE II.

Minimal cooperation as a way to achieve the efficiency in cell-like membrane systems

Cooperation is doubtless a relevant ingredient on rewriting rules based computing models. This paper provides an overview on both classical and newest results studying how cooperation among objects influences the ability of cell-like membrane systems to solve computationally hard problems in an efficient way. In this paper, two types of such membrane systems will be considered: (a) polarizationless P systems with active membranes without dissolution rules when minimal cooperation is permitted in object evolution rules; and (b) cell-like P systems with symport/antiport rules of minimal length. Specifically, assuming that P is not equal to NP, several frontiers of the efficiency are obtained in these two computing frameworks, in such manner that each borderline provides a tool to tackle the P versus NP problem.

A Cuckoo-based Workflow Scheduling Algorithm to Reduce Cost and Increase Load Balance in the Cloud Environment

Workflow scheduling is one of the important issues in implementing workflows in the cloud environment. Workflow scheduling means how to allocate workflow resources to tasks based on requirements and features of the tasks. The problem of workflow scheduling in cloud computing is a very important issue and is an NP problem. The relevant scheduling algorithms try to find optimal scheduling of tasks on the available processing resources in such a way some qualitative criteria when executing the entire workflow are satisfied. In this paper, we proposed a new scheduling algorithm for workflows in the cloud environment using Cuckoo Optimization Algorithm (COA). The aims of the proposed algorithm are reducing the processing and transmission costs as well as maintaining a desirable load balance among the processing resources. The proposed algorithm is implemented in MATLAB and its performance is compared with Cat Swarm Optimization (CSO). The results of the comparisons showed that the proposed algorithm is superior to CSO in discovering optimal solutions.

Recent advances in cloud data centers toward fog data centers

Recent advances in cloud data centers toward fog data centers

Inverse monoids associated with the complexity class NP

We study the P versus NP problem through properties of functions and monoids, continuing the work of [3]. Here we consider inverse monoids whose properties and relationships determine whether P is different from NP, or whether injective one-way functions (with respect to worst-case complexity) exist.

A path to computational efficiency through membrane computing

The search for new mechanisms and tools allowing us to tackle the famous P versus NP problem from new perspectives is an important task, due to the relevance of that problem. The concept of efficiency of computing models is associated with the ability to solve intractable (in a classical sense) problems in polynomial time. Assuming that P≠NP, that concept is equivalent to the capability to solve NP-complete problems in an efficient way. Different frontiers of the efficiency have been given in Membrane Computing in terms of syntactical or semantic ingredients of the models. In particular, in the framework of tissue P systems with cell division using symport/antiport rules, the length of communication rules (passing from length 1 to length 2) provides an optimal borderline of the efficiency.Cell-like P systems with symport/antiport rules and membrane division is a restricted variant of such tissue P systems in both its structure (rooted tree versus undirected graph) and in the way membranes communicate with each other and with the environment. The limitations of efficient computations in such kind of P systems which use non-cooperative communication rules have been previously established. In this paper, a uniform polynomial time solution for the Hamiltonian cycle problem, a well known NP-complete problem, by means of cell-like P systems with membrane division using minimal cooperation in communication rules (at most two objects are involved), is provided. Hence, a new optimal boundary between tractability and NP-hardness, is provided: passing from non-cooperative rules to cooperative rules in cell-like P systems with symport/antiport rules and membrane division amounts to passing from non-efficiency to efficiency.

An Improved Immune Algorithm for Solving Path Optimization Problem in Deep Immune Learning of Gene Network

In order to overcome some defects of the traditional immune algorithm, the immune algorithm was improved for solving a path optimization problem in deep immune learning of a gene network. Firstly, the diversity of the solution population was enhanced in the evolution process by improving the memory cell processing method. Moreover, effective gene information was dynamically extracted from the genes of the excellent antibodies to make good vaccines in the process of immune evolution. Worse antibodies were optimized by vaccinating these antibodies, and the convergence of the immune algorithm to the optimal solution was improved. Finally, the feasibility of the improved immune algorithm was verified in the experimental simulation for solving the classic NP problem in deep immune learning of the gene network.

A hybrid algorithm based on binary chemical reaction optimization and tabu search for feature selection of high-dimensional biomedical data

In recent years, there have been rapid developments in various bioinformatics technologies, which have led to the accumulation of a large amount of biomedical data. The biomedical data can be analyzed to enhance assessment of at-risk patients and improve disease diagnosis, treatment, and prevention. However, these datasets usually have many features, which contain many irrelevant or redundant information. Feature selection is a solution that involves finding the optimal subset, which is known to be an NP problem because of the large search space. Considering this, a new feature selection approach based on Binary Chemical Reaction Optimization algorithm (BCRO) and k-Nearest Neighbors (KNN) classifier is presented in this paper. Tabu search is integrated with CRO framework to enhance local search capacity. KNN is adopted to evaluate the quality of selected candidate subset. The results for an experiment conducted on nine standard medical datasets demonstrate that the proposed approach outperforms other state-of-the-art methods.

The Simplex Algorithm Is NP-Mighty

We show that the Simplex Method, the Network Simplex Method—both with Dantzig’s original pivot rule—and the Successive Shortest Path Algorithm are NP-mighty . That is, each of these algorithms can be used to solve, with polynomial overhead, any problem in NP implicitly during the algorithm’s execution. This result casts a more favorable light on these algorithms’ exponential worst-case running times. Furthermore, as a consequence of our approach, we obtain several novel hardness results. For example, for a given input to the Simplex Algorithm, deciding whether a given variable ever enters the basis during the algorithm’s execution and determining the number of iterations needed are both NP-hard problems. Finally, we close a long-standing open problem in the area of network flows over time by showing that earliest arrival flows are NP-hard to obtain.

Meta-heuristic bus transportation algorithm

Over recent decades, several experience-based mathematical models have been proposed. In addition to collective intelligence, in recent years some efforts have been made to apply human experience-based intelligence to open up a new world of possibilities to design new meta-heuristic algorithms for solving NP problems. In these algorithms instead of only relying on collective intelligence, each individual tries to search for optimal solution based on her or his own experience and others. In this paper, we use a social behavior of humans in transportations to reach their destination and we took experience-based human behavior and smartness of humans as an inspiration to propose our meta-heuristic algorithm and we name it bus transportation algorithm. As a simple example, we restrict our paper to solve a well-known problem integer programming which is known as an NP-Complete problem. Compared to other algorithms, the results in these papers show that our algorithm outperforms PSO (particle swarm optimization), GA (genetic algorithm) and SA (simulated annealing) in terms of efficiency and convergence.

Autonomous vehicle routing problem solution based on artificial potential field with parallel ant colony optimization (ACO) algorithm

An autonomous vehicle routing problem solution (VRPS) algorithm with parallel ant colony optimization (ACO) considering pilot satisfaction is proposed in this paper to solve the problem in traditional autonomous vehicle routing, such as the service quality is affected by longer flying time of pilot due to too much emphasis on cost factors and ignoring of delivery time. First, the flying time of pilot is considered to improve traditional autonomous flight model so as to comprehensively consider autonomous cost and pilot satisfaction. Then, for NP problems in autonomous flight, a parallel ACO algorithm is used for global optimization and design Mapreduce improvement method of parallel ACO, to improve optimization performance of the algorithm and to obtain optimal global solution. At last, a contrast experiment is conducted and the results show that, the algorithm proposed herein can effectively reduce the flying time of pilot and help to improve the service quality.

SMT-Solvers in Action: Encoding and Solving Selected Problems in NP and EXPTIME

SMT-Solvers in Action: Encoding and Solving Selected Problems in NP and EXPTIME

Polynomial-time right-ideal morphisms and congruences

We continue with the functional approach to the P -versus- NP problem, begun in [J. C. Birget, Semigroups and one-way functions, Int. J. Algebra Comput. 25(1–2) (2015) 3–36; J. C. Birget, Infinitely generated semigroups and polynomial complexity, Int. J. Algebra Comput. 26(04) (2016) 727–750.] We previously constructed a monoid [Formula: see text] that is non-regular iff NP [Formula: see text] P . We now construct homomorphic images of [Formula: see text] with interesting properties. In particular, the homomorphic image [Formula: see text] of [Formula: see text] is finitely generated, and is non-regular iff P [Formula: see text] NP . The group of units of [Formula: see text] is the famous Richard Thompson group [Formula: see text].

Comparison and Analysis of Algorithms for the 0/1 Knapsack Problem

The 0/1 knapsack problem is a typical problem in the field of operational research and combinatorial optimization, and it belongs to the NP problem. Research on the solutions of the 0/1 knapsack problem algorithm has very important practical value. This paper first described the 0/1 knapsack problem, and then presented the algorithm analysis, design and implementation of the 0/1 knapsack problem using the brute force algorithm, the greedy algorithm, the genetic algorithm and the dynamic programming algorithm, and compared the four algorithms in terms of algorithm complexity and accuracy. On this basis, the future research directions of the 0/1 knapsack problem were analysed, and we proposed to use the rough set theory to solve the 0/1 knapsack problem. This paper can provide insight for solving the 0/1 knapsack problem and applications.

The role of integral membrane proteins in computational complexity theory

In the framework of Membrane Computing, several tools to tackle the P versus NP problems by means of frontiers of the efficiency expressed in terms of syntactic or semantic ingredients, have been developed. In this paper, an overview of the results in computational complexity theory concerning to membrane systems (tissue-like and cell-like approach) with symport/antiport rules (where objects are transported without evolving), is given. The frontiers are formulated regarding the length of communication rules, the kind of rules implementing the production of an exponential number of cells/membranes in polynomial time, and the role of the environment. An interesting remark of the obtained results refers that the underlying structure to membrane systems (directed graph versus rooted tree) does not matter in this context.

Predatory Search-based Chaos Turbo Particle Swarm Optimisation (PS-CTPSO): A new particle swarm optimisation algorithm for Web service combination problems

Web service combinatorial optimisation is an NP problem (that is, characterised by a nondeterministic polynomial time solution), based on the logical relationship between each service pair. As a consequence, obtaining the best Web service composition scheme is typically a complex task. In this article, we propose the Predatory Search-based Chaos Turbo Particle Swarm Optimisation (PS-CTPSO) algorithm, a chaotic particle swarm optimisation algorithm based on the predatory search strategy, which has significant potential to enhance the overall performance of the Autonomous Cloud.This is achieved by integrating a predatory search and cotangent sequence strategies with the particle swarm optimisation algorithm. More specifically, the PS-CTPSO algorithm identifies a feasible service via a global search, and subsequently, it obtains suitable candidate services within the corresponding chain. The different Web services are grouped into the same class, depending on whether they have the same input and output sets, thus reducing the number of combinations and improving the searching efficiency. In the initialisation phase, the PS-CTPSO component introduces the cotangent method, rather than a random one, which defines individual candidate services within the corresponding classes, creating a feasible service chain. In the update phase, a novel set of rules is used to perturb the velocities and positions of particles for assessing the ideal global search capabilities and adaptability. This effectively overcomes any premature problem, which commonly occurs in traditional PSO (Particle Swarm Optimisation) algorithms, and logic optimisation ensures the diversity of the final combination scheme. In this article, a prototype system (BestWS) is created, based on the directed graph generated by the logic relationships between Web services and the PS-CTPSO, Graph-Based Particle Swarm Optimisation (GB-PSO), Chaos Particle Swarm Optimisation (CS-PSO) and Chaos Particle Swarm Optimisation with Predatory Search strategy (PS-CSPSO) algorithms. The experimental results demonstrate that the cotangent sequence is more suitable than the chaotic one in the field of Web service combination optimisation. Furthermore, compared with the typical implementation of GB-PSO and PS-CSPSO, PS-CTPSO obtains better results, whilst attaining the global optimum with fewer iterations, and with an improved overall ergodicity.

Generic NP-incomplete problems

Ladner in 1975 proved that if P ≠ NP then there exist problems in NP, which are not decidable in polynomial time and not NP-complete. Kapovich, Myasnikov, Schupp and Shpilrain in 2003 developed a theory of generic-case complexity. Generic-case approach considers an algorithmic problem on “most” of inputs instead of all domain and ignores its behaviour on the rest of inputs. In this paper we prove a generic analog of the Ladner’s theorem: If P ≠ NP and P = BPP, then there exists a set S ∈ NP, such that S is not strongly generically decidable in polynomial time and not generically NP-complete. Supported by Russian Science Foundation, grant 17-11-01117.

NEPs Applied to Solve Specific Problems

In the following pages we will use NEPS to solve several small instances of well known NP problems. We will show computational implementations of NEPs.

Construction Low Complexity and Low Delay CDS for Big Data Code Dissemination

The diffusion of codes is an important processing technology for big data networks. In previous scheme, data analysis was conducted for small samples of big data and complex problems that cannot be processed by big data technology. Due to the limited capacity of intelligence device, a better method is to select a set of nodes (intelligence device) to form a connected dominating set (CDS) to save energy, and constructing CDS is proved to be a complete NP problem. However, it is a challenge to reduce the communication delay and complexity for urgent data transmission in big data. In this paper, an appropriate duty cycle control (ADCC) scheme is proposed to reduce communication delay and complexity while improving energy efficient in CDS-based WSNs. In ADCC scheme, the method for constructing CDS is proposed at lower complexity. Nodes in CDS are selected according to the degree of nodes. Then, duty cycle of dominator nodes in CDS is higher than that of dominated nodes, so the communication delay in the proposed scheme is far less than that of previous scheme. The duty cycle of dominated nodes is small to save energy. This is because the number of dominator nodes in CDS is far less than the number of dominated nodes whose duty cycle is small; thus, the total energy consumption of the network is less than that of the previous scheme. As a result, the performance of energy consumption and communication delay and complex have been improved. Its complexity O∑i=0vm−i+2m−2v−s is reduced a lot for big data. The theoretical analysis shows that compared to the previous scheme, the transmission delay can be reduced 25–92% and the energy efficiency is improved by about 80% while retaining network lifetime.