NP Problem Research Articles

Towards Geometry-Preserving Reductions Between Constraint Satisfaction Problems (and other problems in NP)

Towards Geometry-Preserving Reductions Between Constraint Satisfaction Problems (and other problems in NP)

Steiner 3-Wiener Index of Zigzag Polyhex Nanotubes.

Let G be a connected graph and S be a k element subset of the vertex set V(G) of G. Steiner distance is a natural generalization of the usual graph distance. The Steiner-k distance dG(S) between the vertices of S is the minimum size among all connected subgraphs whose vertex set contains S. The generalized indices based on Steiner distances have several applications in the real world. It is a well-known fact that "Steiner Problem" is NP-complete and hence any parameter based on Steiner distance is also an NP problem. The objective of this work is to determine the Steiner 3-Wiener index for an important chemical structure called the zigzag polyhex nanotube. In this paper, we present an algorithm for computing the Steiner 3-Wiener index (SW3) for zigzag polyhex nanotubes. The developed algorithm addresses the complexities associated with exponential increments in the number of vertices as the nanotube's circumference or length expands. The obtained SW3 values for zigzag polyhex nanotubes can be used for Quantitative Structure-Activity Relationship (QSAR) and Quantitative Structure-Property Relationship (QSPR) analyses. We have presented an algorithm and listed the numerical values of SW3 for various parameters of circumference and length of a zigzag polyhex nanotube to facilitate their utilization in QSAR/ QSPR analyses. We have obtained the time complexity for the algorithm, which shows that the SW3 values are computationally intensive. To explain this complex nature, we have used multiple linear regression to fit log SW3 values corresponding to log p and log q, the radius and length of a nanotube. The algorithm addresses the complexities associated with the exponential increase in vertices as the nanotube's circumference or length expands. Furthermore, we provide SW3 values for various parameter combinations up to circumference or length 17, and a general relation to determine the value of SW3, facilitating its utilization in real-world applications. These values serve as crucial descriptors for understanding the structural nuances of zigzag polyhex nanotubes, that find applications in material science, drug design, drug discovery, etc.

Solving NP-complete Problems Efficiently

The P versus NP problem is a fundamental question in computer science. It asks whether problems whose solutions can be quickly verified can also be quickly solved. Here, "quickly" refers to computational time that grows proportionally to the size of the input (polynomial time). While the problem's roots trace back to a 1955 letter from John Nash, its formalization is attributed to Stephen Cook and Leonid Levin. Despite extensive research, a definitive answer remains elusive. Closely tied to this is the concept of NP-completeness. If a single NP-complete problem could be solved efficiently, it would imply that all problems in NP can be solved efficiently, proving that P equals NP. Garey and Johnson defined K-CLOSURE such that for any edge $(u, v)$ in the directed graph, either node $u$ is in the set $V'$ or node $v$ is not in $V'$. This implies that either both nodes are in $V'$ or both are not in $V'$. Our previous work in IPI Letters presented a polynomial-time algorithm for K-CLOSURE. While no errors have been identified in this work, many believe that Garey and Johnson's original definition was incorrect, and their citation of Queyranne was a misunderstanding. Many argue that the empty set serves as a simple counterexample to Garey and Johnson's definition of K-CLOSURE. This paper proposes that K-CLOSURE is actually an NP-complete problem, which would imply that P equals NP.

Note for the P versus NP Problem

P versus NP is considered as one of the most fundamental open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? It was essentially mentioned in 1955 from a letter written by John Nash to the United States National Security Agency. However, a precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. Another major complexity class is NP-complete. It is well-known that P is equal to NP under the assumption of the existence of a polynomial time algorithm for some NP-complete. We show that the Monotone Weighted Xor 2-satisfiability problem (MWX2SAT) is NP-complete and P at the same time. Certainly, we make a polynomial time reduction from every directed graph and positive integer k in the K-CLOSURE problem to an instance of MWX2SAT. In this way, we show that MWX2SAT is also an NP-complete problem. Moreover, we create and implement a polynomial time algorithm which decides the instances of MWX2SAT. Consequently, we prove that P = NP.

Dynamic adaptive quantum approximate optimization algorithm for shallow, noise-resilient circuits

The quantum approximate optimization algorithm (QAOA) is an appealing proposal to solve NP problems on noisy intermediate-scale quantum (NISQ) hardware. Making NISQ implementations of the QAOA resilient to noise requires short ansatz circuits with as few controlled- () gates as possible. Here we present the dynamic adaptive quantum approximate optimization algorithm (Dynamic-ADAPT-QAOA). Our algorithm significantly reduces the circuit depth and the count of standard ADAPT-QAOA, a leading proposal for near-term implementations of the QAOA. Throughout our algorithm, the decision to apply -intensive operations is made dynamically, based on algorithmic benefits. Using density-matrix simulations, we benchmark the noise resilience of ADAPT-QAOA and Dynamic-ADAPT-QAOA. We compute the gate-error probability pgate★ below which these algorithms provide, on average, more accurate solutions than the classical, polynomial-time approximation algorithm by Goemans and Williamson. For small systems with six to ten qubits, we show that pgate★>10−3 for Dynamic-ADAPT-QAOA. Compared to standard ADAPT-QAOA, this constitutes an order-of-magnitude improvement in noise resilience. This improvement should make Dynamic-ADAPT-QAOA viable for implementations on superconducting NISQ hardware, even in the absence of error mitigation. Published by the American Physical Society 2024

Exploring Quantum Computing Paradigm: From Conceptualisation, Initial Adoption to Development

Quantum computing (QC) holds promise for next-generation applications that requires exponential time to solve NP problems. However, even after 25+ years, researchers still struggle with stable error correction solutions for delivering a stable commercialised quantum universal quantum machine. Companies like IBM, Rigetti, and D-Wave have already started offering quantum annealers, intermediate quantum devices based on the qubit. Therefore, researchers believe that QC would be introduced as an extension of classical computers (CC), where CC would offload a specific computational intensive task. Cloud companies, including Amazon, Azure, and IBM, have already begun to provide cloud services where an organisation can use a QC to work on potential applications. This paper systematically analyses the need to provide QC as a service (QCaaS) for potential applications. Furthermore, we discuss the framework on which this service can be offered. Subsequently, we provide a detailed discussion of various toolkits, libraries, and simulators available for QC.

Dynamic range optimization of optoelectronic systems based on quantum mathematical models

A photodiode is a small and low-cost photosensitive sensor that can measure the solar vector through at least three combinations, making it a high-precision solar sensor. How to select the number of photodiodes and determine their layout is a challenge in order to solve the solar vector in any direction in a 360° field of view space as much as possible, the author first discretizes the equal surface area of the 360° field of view space, transforming the infinite sensor layout optimization problem into a finite combinatorial optimization (NP problem is difficult). Then, by establishing multi-objective optimization functions for coverage and uniformity, and combining quantum genetic algorithm to solve the optimal solution. The experimental analysis of the layout effects of different numbers of photodiodes and field of view ranges provides a theoretical basis for optimizing the layout of multiple photodiodes. The experimental results show that selecting 12 to 14 photodiodes can basically achieve a layout without coverage risk and uniform risk.

Graphical representation and hierarchical decomposition mechanism for vertex-cover solution space

NP problems act essential roles in modelling and analysing various complex systems, and representation learning of system individuals and relations has faced the kernel difficulty in understanding the complexity and solving the NP problems. In this paper, solution space organisation of minimum vertex-cover problem is deeply investigated using the famous König-Egérvary (KE) graph and theorem, in which a hierarchical decomposition mechanism named KE-layer structure of general graphs is proposed to reveal the complexity of vertex-cover. To achieve the graphical representation and hierarchical decomposition, an algorithm to verify the KE graph is given by the solution space expression of vertex-cover, and the relation between multi-layer KE graphs and maximal matching is illustrated and proved. Furthermore, a framework to calculate the KE-layer number and approximate the minimal vertex-cover is provided, with different strategies of switching nodes and counting energy. The phase transition phenomenon between different KE-layers is studied with the transition points located, and searching of vertex-cover got by this strategy presents comparable advantage against several other methods. Its efficiency outperforms the existing ones just before the transition point. The graphical representation and hierarchical decomposition provide a new perspective to illustrate the structural organisations of graphs better, and its formation mechanism can help reveal the intrinsic complexity and establish heuristic strategy for large-scale graphs/systems recognition.

Research On Emergency Parcel Transfer and Structure Optimization of E-Commerce Logistics Network Based on Multi-Objective Planning

This paper addresses the problem of urgent forwarding and structural optimization of parcels in e-commerce logistics networks. Firstly, based on the historical data of past freight volumes of different routes, this paper predicts the freight volume forecast data of each route by establishing an ARIMA time series forecast model; secondly, a multi-objective optimization model based on genetic algorithm is established to derive the optimal freight volume allocation scheme after the disappearance of route DC5; again, a multi-objective optimization model based on bat algorithm is established to derive the DC9 route Finally, a multi-objective optimization model based on the bat algorithm was developed to derive the route adjustment and cargo allocation scheme after the disappearance of route DC9. This paper concludes that after the cancellation of the DC5 route, the number of routes that are not in normal operation is 23 and the number of logistics paths that are allocated to new cargo is 56 in order to achieve the most balanced route load possible; after the closure of the DC9 route, 21 new roads are opened and 15 roads are closed, which are in a normal flow state and the transhipment is balanced. This paper has more far-reaching applications for multi-objective large-scale NP problems by establishing a multi-objective optimization model based on a heuristic algorithm, which can reduce the solution time of the calculation.

Improved Bare Bones Particle Swarm Optimization for DNA Sequence Design.

DNA computing has efficient computational power, but requires high requirements on the DNA sequences used for coding, and reliable DNA sequences can effectively improve the quality of DNA encoding. And designing reliable DNA sequences is an NP problem, because it requires finding DNA sequences that satisfy multiple sets of conflicting constraints from a large solution space. To better solve the DNA sequence design problem, we propose an improved bare bones particle swarm optimization algorithm (IBPSO). The algorithm uses dynamic lensing opposition-based learning to initialize the population to improve population diversity and enhance the ability of the algorithm to jump out of local optima; An evolutionary strategy based on signal-to-noise ratio(SNR) distance is designed to balance the exploration and exploitation of the algorithm; Then an invasive weed optimization algorithm with niche crowding(NCIWO) is used to eliminate low-quality solutions and improve the search efficiency of the algorithm. In addition, we introduce the triplet-bases unpaired constraint to further improve the quality of DNA sequences. Finally, the effectiveness of the improved strategy is demonstrated by ablation experiments; and the DNA sequences designed by our algorithm are of higher quality compared with those generated by the four advanced algorithms.

A Protocol for Solutions to DP-Complete Problems through Tissue Membrane Systems

Considering a class R comprising recognizer membrane systems with the capability of providing polynomial-time and uniform solutions for NP-complete problems (referred to as a “presumably efficient” class), the corresponding polynomial-time complexity class PMCR encompasses both the NP and co-NP classes. Specifically, when R represents the class of recognizer presumably efficient cell-like P systems that incorporate object evolution rules, communication rules, and dissolution rules, PMCR includes both the DP and co-DP classes. Here, DP signifies the class of languages that can be expressed as the difference between any two languages in NP (it is worth noting that NP ⊆ DP and co-NP⊆co-DP). As DP-complete problems are believed to be more complex than NP-complete problems, they serve as promising candidates for studying the P vs. NP problem. This outcome has previously been established within the realm of recognizer P systems with active membranes. In this paper, we extend this result to encompass any class R of presumably efficient recognizer tissue-like membrane systems by presenting a detailed protocol for transforming solutions of NP-complete problems into solutions of DP-complete problems.

Analysis of Polynomial Time and Non-Polynomial Time of Algorithms

Abstract: The P vs NP problem is one of the most significant open problems in computer science and mathematics. This problem asks whether every problem that can be solved in polynomial time can also be verified in polynomial time. The purpose of this research paper is to explore the P vs NP problem and its relevance in the analysis of algorithms. We will discuss the techniques used to design and analyze algorithms, such as divide-and-conquer, dynamic programming, and greedy algorithms, and their relation to the P vs NP problem. We will also examine some examples of polynomial-time algorithms and NP-hard problems and analyze their time and space complexity, addition to which we will analyze the NP-Complete Problem and finally looking the current scenario of the P & NP and stating its significance.

Offloading Strategy of Multi-Service and Multi-User Edge Computing in Internet of Vehicles

An edge computing offloading strategy was proposed with the goal of addressing the issue of low edge computing efficiency and service quality in the multi-service and multi-user intersections of networked vehicles. This strategy took into account all relevant factors, including the matching of users and service nodes, offloading ratio, bandwidth and computing power resource allocation, and system energy consumption. It is mainly divided into 2 tasks: (1) Service node selection: A fuzzy logic-based service node selection algorithm (SNFLC) is proposed. The linear equation for node performance value is determined through fuzzy reasoning by specifying three performance indexes as input. Gradient descent method is used to find the optimal value of the objective function, and the Lyapunov criterion coefficient is introduced to improve the stability of the algorithm. (2) Offload ratio and resource allocation are solved: The coupling between offload ratio and bandwidth resource allocation is confirmed by relaxing integer variables because the optimization goal problem is a NP problem, and the issue is divided into two sub-problems. At the same time, a low-complexity alternate iteration resource allocation algorithm (LC-IRA) is proposed to solve the bandwidth resource and computational power resource allocation. According to simulation results, the performance of genetic ant colony algorithm (G_ACA), non orthogonal multiple access technology (NOMA) and LC-IRA are improved by 26.5%, 31.37%, and 45.52%, respectively, compared with the random unloading allocation (RUA) and average distribution (AD).

On Exponential-time Hypotheses, Derandomization, and Circuit Lower Bounds

The Exponential-Time Hypothesis (ETH) is a strengthening of the 𝒫 ≠ 𝒩𝒫 conjecture, stating that 3- SAT on n variables cannot be solved in (uniform) time 2 εċ n , for some ε > 0. In recent years, analogous hypotheses that are “exponentially strong” forms of other classical complexity conjectures (such as 𝒩𝒫⊈ ℬ𝒫𝒫 or co 𝒩𝒫⊈𝒩𝒫) have also been introduced and have become widely influential. In this work, we focus on the interaction of exponential-time hypotheses with the fundamental and closely related questions of derandomization and circuit lower bounds . We show that even relatively mild variants of exponential-time hypotheses have far-reaching implications to derandomization, circuit lower bounds, and the connections between the two. Specifically, we prove that: (1) The Randomized Exponential-Time Hypothesis (rETH) implies that ℬ𝒫𝒫 can be simulated on “average-case” in deterministic (nearly-)polynomial-time (i.e., in time 2 Õ(log( n )) = n loglog( n ) O(1) ). The derandomization relies on a conditional construction of a pseudorandom generator with near-exponential stretch (i.e., with seed length Õ(log ( n ))); this significantly improves the state-of-the-art in uniform “hardness-to-randomness” results, which previously only yielded pseudorandom generators with sub-exponential stretch from such hypotheses. (2) The Non-Deterministic Exponential-Time Hypothesis (NETH) implies that derandomization of ℬ𝒫𝒫 is completely equivalent to circuit lower bounds against ℰ, and in particular that pseudorandom generators are necessary for derandomization. In fact, we show that the foregoing equivalence follows from a very weak version of NETH, and we also show that this very weak version is necessary to prove a slightly stronger conclusion that we deduce from it. Last, we show that disproving certain exponential-time hypotheses requires proving breakthrough circuit lower bounds. In particular, if CircuitSAT for circuits over n bits of size poly(n) can be solved by probabilistic algorithms in time 2 n /polylog(n) , then ℬ𝒫ℰ does not have circuits of quasilinear size.

IMPLEMENTATION OF QUANTUM ARITHMETIC OPERATIONS WITH INTEGER CHARACTERS USING THE QUANTUM FOURIER TRANSFORM

It has been proven that a quantum computer is superior to an electronic computer in solving some NP problems. Based on quantum operations, this article proposes a new quantum sum and quantum multiplication, and then the floating point quantum multiplier and quantum sum are created on the basis of fixed point number operations. These studies lay the foundation for the quantum implementation of digital filters. This article provides a new way to calculate the summator on a quantum computer. This method uses the quantum Fourier transform (QFT) and reduces the number of qubits needed to be added by eliminating the need to temporarily transfer bits. This approach also allows you to add a classical number to a quantum superposition without encoding a classical number in a quantum register. This method also allows for mass parallelization during its execution. Adding and multiplying capabilities based on QFT are improved with some changes. The proposed operations are compared with the operations of close quantum arithmetic. TRANSLATE with x English Arabic Hebrew Polish Bulgarian Hindi Portuguese Catalan Hmong Daw Romanian Chinese Simplified Hungarian Russian Chinese Traditional Indonesian Slovak Czech Italian Slovenian Danish Japanese Spanish Dutch Klingon Swedish English Korean Thai Estonian Latvian Turkish Finnish Lithuanian Ukrainian French Malay Urdu German Maltese Vietnamese Greek Norwegian Welsh Haitian Creole Persian   //   TRANSLATE with COPY THE URL BELOW Back EMBED THE SNIPPET BELOW IN YOUR SITE Enable collaborative features and customize widget: Bing Webmaster Portal Back //     Язык этой страницы: Английский   Перевести на Русский         Азербайджанский Албанский Амхарский Английский Арабский Армянский Африкаанс Бенгальский Бирманский Болгарский Валлийский Венгерский Вьетнамский Греческий Гуджарати Датский Иврит Индонезийский Исландский Испанский Итальянский Казахский Каннада Каталанский Китайский (традиционный) Китайский (упрощенный) Корейский Креольский (гаити) Курманджи Кхмерский Лаосский Латышский Литовский Малагасийский Малайский Малаялам Мальтийский Маори Маратхи Немецкий Непальский Нидерландский Норвежский Панджаби Персидский Польский Португальский Пушту Румынский Русский Самоанский Словацкий Словенский Тайский Тамильский Телугу Турецкий Украинский Урду Финский Французский Хинди Хорватский Чешский Шведский Эстонский Японский   Всегда переводить Английский на РусскийPRO Никогда не переводить Английский Никогда не переводить jpcsip.kaznu.kz

On the computational efficiency of tissue P systems with evolutional symport/antiport rules

Tissue P systems with evolutional symport/antiport rules are a variant of tissue P systems, where objects are communicated through regions by symport/antiport rules, and objects may evolve during this process. It is known that such systems are able to solve NP problems in a polynomial time (and exponential space), when cell division is allowed. In this work, we continue to investigate the computational complexity aspects for tissue P systems with evolutional symport/antiport rules. We prove that problems beyond NP can also be solved. In particular, we show that deterministic systems of this type are able to solve all problems in the complexity class PP. Moreover, if non-deterministic systems are considered, then all problems in the class PSPACE can be solved.

Solving a new NP-Complete problem that resembles image pattern recognition using deep learning

In computer science, non-deterministic polynomialtime
 (NP) denotes the set of problems for which a
 solution might or might not be found quickly but can
 be checked quickly. We also call the set of problems
 in NP that are at least as hard as any other NP problem
 non-deterministic polynomial-time complete (NPcomplete).
 Although not known if they can be solved
 quickly, NP-complete problems can be converted
 into one another quickly. A prominent and practical
 example is the protein folding problem, which is a
 problem of determining the shape and function of
 proteins. In this paper, we discovered and provided
 a mathematical proof of a new NP-complete problem,
 that we named 3-Grid Pattern Decision Problem (3-
 GPDP). 3-GPDP is a decision problem that asks if a
 specific kind of pattern exists or not on a grid/matrix
 of numbers consisting of zeros and ones, much like
 image recognition. We hypothesized that a neural net
 would be able to solve 3-GPDP problems with high
 accuracy and low loss when trained. In support of
 our hypothesis, our experiment resulted in a neural
 net that performed with 84% accuracy and 0.14 loss
 without underfitting or overfitting. Moreover, there
 was also an increase in accuracy and decrease in
 loss with more training data. As a result, since neural
 networks are effective at solving 3-GPDP problems,
 which are NP-complete, then we can convert important
 NP-complete problems into 3-GPDP problems, solve
 the 3-GPDP problems using neural networks, and
 convert the solution back to the solution of the initial
 problem, quickly.

Understanding of P vs NP Problem: With Extension of the Continuum Hypothesis

Understanding of P vs NP Problem: With Extension of the Continuum Hypothesis

Thermodynamic Perspectives on Computational Complexity: Exploring the P vs. NP Problem

Thermodynamic Perspectives on Computational Complexity: Exploring the P vs. NP Problem

AI and P Versus NP problem a new method based on artificial intelligence brings us closer to the solution of most important open problem in the theoretical computer science

AI and P Versus NP problem a new method based on artificial intelligence brings us closer to the solution of most important open problem in the theoretical computer science