NP Problem Research Articles

Robust Monocular Pose Tracking of Less-Distinct Objects Based on Contour-Part Model

Due to the lack of distinctiveness to the background, robust monocular 6DOF pose tracking of less-distinct objects remains an important open problem. In this paper, we firstly analyze the object distinctiveness in the tracking process. Then, we propose a novel contour-part model based robust monocular pose tracking method for less-distinct objects. This paper uses the traditional contour feature for pose tracking in a novel strategy called contour part model. First, the contour part model is built by segmenting the projected contour rendered from the 3D model into contour segments of a certain length adaptively according to the Shi-Tomasi cornerness scores. Then, the correspondence is detected in the input image for each contour part by gradient orientation based template matching. Finally, pose tracking is achieved by solving the PnP problem. Experiment results on semi-synthetic and real images show that the proposed method performs better than the existing methods when pose tracking less-distinct objects and shows great robustness toward interference. Additionally, we combine the edge feature and the regional feature in a simple strategy. The overall performance of the fused method is boosted according to the experimental results on the RBOT dataset. The fact shows that the fusion of the edge and regional features has great potential for improving tracking performance.

Computational complexity of flat and generic Assumption-Based Argumentation, with and without probabilities

Reasoning with probabilistic information has recently attracted considerable attention in argumentation, and formalisms of Probabilistic Abstract Argumentation (PAA), Probabilistic Bipolar Argumentation (PBA) and Probabilistic Structured Argumentation (PSA) have been proposed. These foundational advances have been complemented with investigations on the complexity of some approaches to PAA and PBA, but not to PSA. We study the complexity of an existing form of PSA, namely Probabilistic Assumption-Based Argumentation (PABA), a powerful, implemented formalism which subsumes several forms of PAA and other forms of PSA. Specifically, we establish membership (general upper bounds) and completeness (instantiated lower bounds) of reasoning in PABA for the class FP#P (of functions with a #P-oracle for counting the solutions of an NP problem) with respect to newly introduced probabilistic verification, credulous and sceptical acceptance function problems under several ABA semantics. As a by-product necessary to establish PABA complexity results, we provide a comprehensive picture of the ABA complexity landscape (for both flat and generic, possibly non-flat ABA) for the classical decision problems of verification, existence, credulous and sceptical acceptance under those ABA semantics.

A Robust Visual Localization Method With Unknown Focal Length Camera

PnP problem is well researched in many fields, such as computer vision. It is considered the fundamental method to solve the key problems of robot SLAM. However, in pedestrian visual localization, uncalibrated PnP (UPnP), specifically PnP with unknown focal length (PnPf) is more suitable for solving the problem. Recently, a few researchers proposed some methods to alleviate this problem. However, the localization accuracy of the existing methods is not satisfied when image pixel noise is larger. In other words, RANSAC should be running before solving the PnPf problem to get less noisy input, which means the localization delay increases inevitably. In this paper, we propose a more robust method for solving the PnPf problem without the help of RANSAC based on Gröbner basis and convex optimization. We build a Gröbner basis solver on the offline stage with one instance in the prime field. Then, we substitute the coefficients with real value and find multiple solutions on the online stage. Finally, we construct a convex optimization program to seek the final robust solution to PnPf problem. The other purpose of this paper is to provide a second-level localization experience for the end-user. The simulation result shows that our method can give a localization solution, which is more reliable than benchmark methods by both synthetic and real data verified.

Feature Selection Algorithm for High-dimensional Biomedical Data Using Information Gain and Improved Chemical Reaction Optimization

Background: There have been rapid developments in various bioinformatics technologies, which have led to the accumulation of a large amount of biomedical data. However, these datasets usually involve thousands of features and include much irrelevant or redundant information, which leads to confusion during diagnosis. Feature selection is a solution that consists of finding the optimal subset, which is known to be an NP problem because of the large search space. Objective: For the issue, this paper proposes a hybrid feature selection method based on an improved chemical reaction optimization algorithm (ICRO) and an information gain (IG) approach, which called IGICRO. Methods: IG is adopted to obtain some important features. The neighborhood search mechanism is combined with ICRO to increase the diversity of the population and improve the capacity of local search. Results: Experimental results of eight public available data sets demonstrate that our proposed approach outperforms original CRO and other state-of-the-art approaches.

Analysing State-based Models for AI Problems

AI problems which can be solved using a state-based model are a significant portion, covering most NP problems. Although the strategies required to solve such problems are well documented and researched, the model itself is seldom analysed, being considered either secondary or too abstract to tackle in a systematic analysis. Early languages such as PDDL and the many later variants, allow users to describe a state-based model and use a type of exhaustive strategy (usually BFS) to check if that model can solve a defined problem. More recently, SMT-bounded model checking solutions have been employed, a new, generalized approach is described in this paper. Another new contribution described in this paper uses a state classifier to group generated states and thus simplify an exhaustive search for a solution. This allows us to build a complete problem-space having each state within labelled as belonging or not to any path to the goal of the problem.

Topology Agnostic Bounds on Minimum Requirements for Network Failure Identification

In Boolean Network Tomography (BNT), node identifiability is a crucial property that reflects the possibility of unambiguously classifying the state of the nodes of a network as ’working’ or ’failed’ through end-to-end measurement paths. Designing a monitoring scheme satisfying network identifiability is an NP problem. In this article, we provide theoretical bounds on the minimum number of necessary measurement paths to guarantee identifiability of a given number of nodes. The bounds take into consideration two different classes of routing schemes (arbitrary and consistent routing) as well as quality of service (QoS) requirements. We formally prove the tightness of such bounds for the arbitrary routing scheme, and provide an algorithmic approach to the design of network topologies and path deployment that meet the discussed limits. Due to the computational complexity of the optimal solution, We evaluate the tightness of our lower bounds by comparing their values with an upper bound, obtained by a state-of-the-art heuristic for node identifiability. For our experiments we run extensive simulations on both synthetic and real network topologies, for which we show that the two bounds are close to each other, despite the fact that the provided lower bounds are topology agnostic.

AN APPLICATION OF METAHEURISTIC OPTIMIZATION ALGORITHMS FOR SOLVING THE FLEXIBLE JOB-SHOP SCHEDULING PROBLEM

Abstract. The Flexible Job Planning (FJSP) problem is another planning and scheduling problem. It is a continuation of the classic problem of scheduling jobs, where each operation can be performed on different machines, while the processing time depends on the machine being used. FJSP is a difficult NP problem that consists of two sub-problems, scheduling problems and scheduling operations. The paper presents a model for solving FJSP based on meta-heuristic algorithms: Genetic algorithm (GA), Tabu search (TS) and Ant colony optimization (ACO). The efficiency of the approach in solving the aforementioned problem is reflected in the flexible search of space and the choice of dominant solutions. The results of the computation are graphically represented on the Gantt chart.

RPCA-based real-time speech and music separation method

The improvement of the performance of online separating speech and music is an NP problem and the separation optimization increases the complexity of the method in a Robust Principal Component Analysis (RPCA) method which is time consuming in big size matrix computations. This paper presents a RPCA-based speech and music separation method to reduce the amount of computational complexity and be robust to artificial noise by proposing two novel algorithms. The key idea of our real-time method is designing a novel random singular value decomposition algorithm in a non-convex optimization environment to significantly decrease the complexity of previous RPCA methods from min(mn2,m2n)flops to mnrflops where r≪min(m,n) to obtain better performance and get qualified results. Experimental results of different datasets compared with the best state-of-the-art method show that the proposed method is more reliable and achieves an average 339% speedup by the significant reduction of computational complexity, increases the quality of the speech signal by 295%, improves the quality of the music signal by 244% and the robustness of artificial noise without needing any learning technique or requiring particular features.

The Parallel Quantum Algorithm for the Class of Optimization

For the given n numbers without any other prior information, how to obtain the minimum norm of them only by assigning their signs before them? Moreover, how to know one number is the multiplication of which ones in the given n numbers? In classical solutions, enumeration is the only way via trying one by one, whose complexity is about [Formula: see text] and this is a NP problem. In this paper, the parallel quantum algorithm is proposed to solve the two questions shown in above. Through the quantum design of linear expressions of angles in parallel circuits, only [Formula: see text] time’s quantum operations and about [Formula: see text] times’ quantum measurements in the average will give the correct answer in the successful probability of 0.97 instead of the traditional [Formula: see text] times. The example and theoretical analysis demonstrate the efficiency of the proposed method.

Computing with SN P systems with I/O mode

P systems were introduced more than two decades ago by Gheorghe Pǎun. They are known as nondeterministic maximally parallel computing models. Most of their variants are proved to be capable of solving NP problems in polynomial time. This work focuses on using neural-like P systems to simulate uniform sequential computing models. In particular, we consider a so-called Spiking Neural P module (SN P module) computing finite-state functions. We define and characterize a so-called (SN) P automatic sequence by SN P modules.

Taxonomy Genetic Algorithm For Implementation Partially Mapped Crossover In Travelling Salesman Problem

Genetic algorithmhasvarious process are carried out to get optimal results in solving the problem of traveling salesman problemTravelling salesman problem (TSP) as known as combinatorial NP problem. Salesman given a map that he has accomplished all cities only once by minimized the total of distance and he has to return to the first city. By describing the taxonomy in genetic algorithm, it can avoid confusion in understanding the various classifications that exist in the genetic algorithm operator. This paper explains one of the parts from genetic algorithm is crossover. Crossover being important step in genetic algorithm. Commonly mechanism crossover replaces two selected chromosome which part from two parent’s individual randomly position, generate random number interval 0-1. Crossover occur for each individual by determining the probability of the crossover. If the probability crossover is smaller than random number, there is no crossover process. Partially mapped crossover is part of the taxonomy of genetic algorithms whose implementations can be applied in a variety of problem solving including in the travelling salesman problem. The test results of this researchusing pc 0.25 and pm 0,1 with tsp eil51 data, it was found that the optimal route average value was 4069.34 and the best fitness average was 2.46E-04, while for the eil76 test data the optimal route average value was 6844.4. and the average best fitness value of 1.46E-04.

Seeking computational efficiency boundaries: the Păun’s conjecture

In 2005, Gh. Păun raised an interesting question concerning the role of electrical charges in P systems with active membranes from a complexity point of view. Specifically, he formulated a question about the computational efficiency of polarizationless P systems with dissolution rules and division rules only for elementary membranes. Several approaches have been carried out, and some partial answers have been given. This is probably the most important open problem in computational complexity theory in the framework of Membrane Computing. The study of the efficiency of membrane systems has been a very fruitful area, providing not only the above-stated partial answers, but also several frontiers of efficiency to tackle the P vs NP problem. In this work, a survey on classical and current results on complexity aspects is given, emphasizing on the frontiers of efficiency and the ingredients taken into account for each of them.

SLPA-based parallel overlapping community detection approach in large complex social networks

Performance improvement of community detection is an NP problem in large social networks analysis where by integrating the overlapped communities’ information and modularity maximization increases the time complexity and memory usage. This paper presents an online parallel overlapping community detection approach based on a speaker-listener propagation algorithm by proposing a novel parallel algorithm and applying three new metrics. This approach is presented to improve modularity and expand scalability for getting a significantly speedup in low time-consuming and usage memory through an agent-based parallel implementation in a multi-core architecture. The key ideas of our approach are increasing the communities’ conductance score, limiting the speaking-listening stages and executing a strategic updating order to develop a speaker-listeners label propagation algorithm for getting better speedup and semi-deterministic results without using prior training or requiring particular predefined features. Experimental results of used large datasets compared with state-of-the-art algorithms show that the proposed method is extremely convergence and achieves an average 820% speedup in the label propagation algorithm, and significantly improves the modularity that are effective in finding better overlapping communities in a linear time complexity O(m) and lower usage memory O(n).

The Cross-Entropy Method for the Winner Determination Problem in Combinatorial Auctions

The combinatorial auction is one of the important methods used for multi-item auctions, and the solution to the winner determination problem (WDP) is the key factor in the widespread application of combinatorial auctions. This paper explores the use of the cross-entropy method to solve the WDP, which is an NP problem. The performance of the proposed approach is evaluated on the basis of two well-known benchmark test cases. The experimental results show that, compared with the genetic algorithm and the particle swarm optimization algorithm, the cross-entropy（CE）method has the advantages of a higher success rate and a shorter time for solving the WDP. Therefore, the CE method provides a high-quality solution for the effective solution of the problem of determining winning bids in combined auctions.

Qubits’ mapping and routing for NISQ on variability of quantum gates

Rapid development has taken place in quantum algorithms, but few of them can be implemented directly on the quantum computer because of the coupling constraint and high error rates of quantum computer operations. Transforming a circuit into an executable one on the quantum computer with the highest fidelity is an NP problem. Therefore, the algorithm tackling the mapping and routing problem of qubits is needed. Following the policy of VQA, a heuristic algorithm to solve the problem is proposed. The algorithm uses the error score derived from quantum operation’s error rate as the heuristic cost. Combining SWAP gates, physical CNOT gates, remote CNOT gates and inverse CNOT gates, the algorithm transforms the input circuit into an executable output circuit on the quantum computer with lower error score in acceptable execution time and moves forward from local optimal to global optimal.

The Optimization of Feature Selection Based on Chaos Clustering Strategy and Niche Particle Swarm Optimization

With the rapid increase of the data size, there are increasing demands for feature selection which has been a powerful tool to handle high-dimensional data. In this paper, we propose a novel feature selection of niche particle swarm optimization based on the chaos group, which is used for evaluating the importance of feature selection algorithms. An iterative algorithm is proposed to optimize the new model. It has been proved that solving the new model is equivalent to solving a NP problem with a flexible and adaptable norm regularization. First, the whole population is divided into two groups: NPSO group and chaos group. The two groups are iterated, respectively, and the global optimization is updated. Secondly, the cross-iteration of NPSO group and chaos group avoids the particles falling into the local optimization. Finally, three representative algorithms are selected to be compared with each other in 10 UCI datasets. The experimental results show that the feature selection performance of the algorithm is better than that of the comparison algorithm, and the classification accuracy is significantly improved.

A Proof “P≠NP” for P vs. NP Problem by Multiple-Tape Turing-Machine

P vs. NP problem is very important research direction in computation complexity theory. In this paper author, by an engineer’s viewpoint, establishes universal multiple-tape Turing-machine and k-homogeneous multiple-tape Turing-machine, and by them we can obtain an unified mathematical model for algorithm-tree, from the unified model for algorithm-tree, we can conclude that computation complexity for serial processing NP problem if under parallel processing sometimes we can obtain P=NP  in time-complexity, but that will imply another NP, non-deterministic space-complexity NP, i.e., under serial processing P≠NP  in space-complexity, and the result is excluded the case of NP problem that there exists a faster algorithm to replace the brute-force algorithm, and hence we can proof that under parallel processing time-complexity is depended on space-complexity, and vice verse, within P vs. NP problem, this point is just the natural property of P vs. NP problem so that “P≠NP ”.

An algebraic expression of the number partitioning problem

In this paper we investigate the number partitioning problem, using the tropical semiring (max-plus algebra). We show that the problem is reduced to deciding whether one of integers is a solution of a tropical analogue of algebraic equations with coefficients composed of other integers. For n up to 6 we derive concretely and explicitly the equation and its solution set. The derivation requires only routine algebraic computations, so can be applied for n larger than 6. Our approach based on max-plus algebra reveals the mathematical structure of the problem and provides a new view point for the P versus NP problem, since the problem is well-known to be NP-complete.

Indoor Positioning Using PnP Problem on Mobile Phone Images

As people grow accustomed to effortless outdoor navigation, there is a rising demand for similar possibilities indoors as well. Unfortunately, indoor localization, being one of the requirements for navigation, continues to be a problem without a clear solution. In this article, we are proposing a method for an indoor positioning system using a single image. This is made possible using a small preprocessed database of images with known control points as the only preprocessing needed. Using feature detection with the SIFT (Scale Invariant Feature Transform) algorithm, we can look through the database and find an image that is the most similar to the image taken by a user. Such a pair of images is then used to find coordinates of a database of images using the PnP problem. Furthermore, projection and essential matrices are determined to calculate the user image localization—determining the position of the user in the indoor environment. The benefits of this approach lie in the single image being the only input from a user and the lack of requirements for new onsite infrastructure. Thus, our approach enables a more straightforward realization for building management.

Four Arithmetic Operations on the Quantum Computer

Quantum computer has been proved to be superior to electronic computer in solving some NP problems. Based on the former quantum adder, this paper proposes a new quantum adder and quantum subtracter, and then designs a fixed-point quantum multiplier and a fixed-point quantum divider based on fixed-point number operations. Four arithmetic units are presented using quantum gate circuits. These researches lay a foundation for the quantum implementation of digital filters.