What on Earth is an NP Problem?

2021 ◽  
pp. 109-118
Author(s):  
Malcolm E Lines
Keyword(s):  
Np Problem

Bounds on the partition dimension of convex polytopes

2020 ◽  
Vol 23 ◽  
Author(s):  
Jia-Bao Liu ◽  
Muhammad Faisal Nadeem ◽  
Mohammad Azeem
Keyword(s):  
Combinatorial Optimization ◽  
Computer Science ◽  
Facility Location ◽  
Robot Navigation ◽  
Convex Polytopes ◽  
Pharmaceutical Chemistry ◽  
Resolving Set ◽  
Minimum Number ◽  
Partition Dimension ◽  
Np Problem

Aims and Objective: The idea of partition and resolving sets plays an important role in various areas of engineering, chemistry and computer science such as robot navigation, facility location, pharmaceutical chemistry, combinatorial optimization, networking, and mastermind game. Method: In a graph to obtain the exact location of a required vertex which is unique from all the vertices, several vertices are selected this is called resolving set and its generalization is called resolving partition, where selected vertices are in the form of subsets. Minimum number of partitions of the vertices into sets is called partition dimension. Results: It was proved that determining the partition dimension a graph is nondeterministic polynomial time (NP) problem. In this article, we find the partition dimension of convex polytopes and provide their bounds. Conclusion: The major contribution of this article is that, due to the complexity of computing the exact partition dimension we provides the bounds and show that all the graphs discussed in results have partition dimension either less or equals to 4, but it cannot been be greater than 4.

Zygmunt Zawirski wśród inżynierów i organizatorów – cz. II

2021 ◽  
pp. 33-40
Author(s):  
Alojzy Czech
Keyword(s):  
Np Problem

<p xss=removed><span xss=removed>W części pierwszej zostały przypomniane związki Zygmunta Zawirskiego z psychologią eksperymentalną jako podstawą dla zastosowań w pracy przemysłowej na tle narastającego dorobku z zakresu filozofii nauki. Następnym etapem obecności filozofa w środowisku techników było powierzenie Zawirskiemu roli organizatora i kierownika pracowni psychotechnicznej dla młodzieży rękodzielniczej z misją prowadzenia poradnictwa zawodowego. Omówienia kierunków jej działania, programów i przyrządów, w które została wyposażona, Zawirski dokonał na II Zjeździe Polskim Naukowej Organizacji w 1928 roku w Warszawie. Przypomnieniu tego mało znanego fragmentu z biografii uczonego w głównej mierze poświęcone jest niniejsze opracowanie.  Kooperacja ze środowiskiem organizatorskim została jednak przerwana ze względu na powołanie Zawirskiego na Katedrę Teorii i Metodologii Nauk w Uniwersytecie Poznańskim. Jego dokonania w zakresie filozofii nauki, zastosowań współczesnej logiki oraz metodologii znacząco wtedy narastały – co w zarysie również zostało przedstawione – ale jeszcze wtedy znalazło się miejsce na kontynuację zainteresowań psychologią praktyczną poprzez tłumaczenia literatury z tej dziedziny z języka francuskiego. Należy także mieć na uwadze, że wiele rozwiązań z ogólnonaukowego dorobku Zawirskiego, jak np. problem logiki indukcji czy sugestie w zakresie syntezy naukowej po dziś mogą służyć pomocą adeptom uprawiania nauki.</span><br></p>

scholarly journals Computing Simplicial Depth by Using Importance Sampling Algorithm and Its Application

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Fanyu Meng ◽  
Wei Shao ◽  
Yuxia Su
Keyword(s):  
Importance Sampling ◽  
Testing Machine ◽  
Exact Algorithm ◽  
Real Data ◽  
Exact Algorithms ◽  
Approximate Algorithm ◽  
Sampling Algorithm ◽  
Simplicial Depth ◽  
Low Efficiency ◽  
Np Problem

Simplicial depth (SD) plays an important role in discriminant analysis, hypothesis testing, machine learning, and engineering computations. However, the computation of simplicial depth is hugely challenging because the exact algorithm is an NP problem with dimension d and sample size n as input arguments. The approximate algorithm for simplicial depth computation has extremely low efficiency, especially in high-dimensional cases. In this study, we design an importance sampling algorithm for the computation of simplicial depth. As an advanced Monte Carlo method, the proposed algorithm outperforms other approximate and exact algorithms in accuracy and efficiency, as shown by simulated and real data experiments. Furthermore, we illustrate the robustness of simplicial depth in regression analysis through a concrete physical data experiment.

The Golden Ticket

2017 ◽  
Author(s):  
Lance Fortnow
Keyword(s):  
Traveling Salesman ◽  
Open Problems ◽  
Mathematical Objects ◽  
Shortest Route ◽  
The Status ◽  
Np Problem

This introductory chapter provides an overview of the P versus NP problem. The P versus NP problem asks, among other things, whether one can quickly find the shortest route for a traveling salesman. P and NP are named after their technical definitions, but it is best not to think of them as mathematical objects but as concepts. “NP” is the collection of problems that have a solution that one wants to find. “P” consists of the problems to which one can find a solution quickly. “P = NP” means one can always quickly compute these solutions, like finding the shortest route for a traveling salesman. “P ≠ NP” means one cannot. Ultimately, the P versus NP problem has achieved the status of one of the great open problems in all of mathematics.

scholarly journals Computational Complexity Theory and the Philosophy of Mathematics†

2019 ◽  
Vol 27 (3) ◽  
pp. 381-439
Author(s):  
Walter Dean
Keyword(s):  
Computational Complexity ◽  
Computer Science ◽  
Complexity Theory ◽  
Philosophy Of Mathematics ◽  
Computability Theory ◽  
Computational Complexity Theory ◽  
Mathematical Problems ◽  
Np Problem

Abstract Computational complexity theory is a subfield of computer science originating in computability theory and the study of algorithms for solving practical mathematical problems. Amongst its aims is classifying problems by their degree of difficulty — i.e., how hard they are to solve computationally. This paper highlights the significance of complexity theory relative to questions traditionally asked by philosophers of mathematics while also attempting to isolate some new ones — e.g., about the notion of feasibility in mathematics, the $\mathbf{P} \neq \mathbf{NP}$ problem and why it has proven hard to resolve, and the role of non-classical modes of computation and proof.

Ant Colony Optimization for Factory Layout

2012 ◽  
Vol 591-593 ◽  
pp. 758-761
Author(s):  
Xiu Zeng ◽  
Qian Li Ma
Keyword(s):  
Genetic Algorithm ◽  
Simulated Annealing ◽  
Ant Colony Optimization ◽  
Heuristic Algorithms ◽  
Mean Value ◽  
Ant Colony ◽  
Logistics Cost ◽  
The Mean ◽  
Factory Layout ◽  
Np Problem

Factory layout is NP problem[1]. There are many methods to solve it ,such as engineering diagram, flow chart method, various heuristic algorithms, SA( simulated annealing) and GA(genetic algorithm) [2].ACO (ant colony optimization) is used to solve it in this paper. The logistics costs exist between two workshops that are treated as pheromone that guides ants to search the best solution. Smaller logistics cost is, stronger the two workshops of relation is. In the process of optimization theworkshop with low logistics cost is more likely to be chosen, which minimizes the system logistics cost. Compared with GA, ACO has the advantage in speed. The mean value of the solution, the best solution, the worst solution is better too. More the number of workshop is, more obvious the superiority is.

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