scholarly journals Tries-Based Parallel Solutions for Generating Perfect Crosswords Grids

Algorithms ◽  
2022 ◽  
Vol 15 (1) ◽  
pp. 22
Author(s):  
Virginia Niculescu ◽  
Robert Manuel Ştefănică
Keyword(s):  
Data Structures ◽  
Execution Time ◽  
Grid Generation ◽  
Good Opportunity ◽  
Complete Problem ◽  
3D Space ◽  
Black Boxes ◽  
Np Complete

A general crossword grid generation is considered an NP-complete problem and theoretically it could be a good candidate to be used by cryptography algorithms. In this article, we propose a new algorithm for generating perfect crosswords grids (with no black boxes) that relies on using tries data structures, which are very important for reducing the time for finding the solutions, and offers good opportunity for parallelisation, too. The algorithm uses a special tries representation and it is very efficient, but through parallelisation the performance is improved to a level that allows the solution to be obtained extremely fast. The experiments were conducted using a dictionary of almost 700,000 words, and the solutions were obtained using the parallelised version with an execution time in the order of minutes. We demonstrate here that finding a perfect crossword grid could be solved faster than has been estimated before, if we use tries as supporting data structures together with parallelisation. Still, if the size of the dictionary is increased by a lot (e.g., considering a set of dictionaries for different languages—not only for one), or through a generalisation to a 3D space or multidimensional spaces, then the problem still could be investigated for a possible usage in cryptography.

scholarly journals Time-Free Solution to SAT Problem by Tissue P Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Yueguo Luo ◽  
Zhongyang Xiong ◽  
Guanghua Zhang
Keyword(s):  
Intercellular Communication ◽  
Execution Time ◽  
Efficient Solution ◽  
Point Of View ◽  
P Systems ◽  
Free Solution ◽  
Complete Problem ◽  
Np Complete ◽  
First Time ◽  
Computing Models

Tissue P systems are a class of computing models inspired by intercellular communication, where the rules are used in the nondeterministic maximally parallel manner. As we know, the execution time of each rule is the same in the system. However, the execution time of biochemical reactions is hard to control from a biochemical point of view. In this work, we construct a uniform and efficient solution to the SAT problem with tissue P systems in a time-free way for the first time. With the P systems constructed from the sizes of instances, the execution time of the rules has no influence on the computation results. As a result, we prove that such system is shown to be highly effective for NP-complete problem even in a time-free manner with communication rules of length at most 3.

scholarly journals Anti-unification in Constraint Logic Programming

2019 ◽  
Vol 19 (5-6) ◽  
pp. 773-789 ◽  
Author(s):  
GONZAGUE YERNAUX ◽  
WIM VANHOOF
Keyword(s):  
Logic Programming ◽  
Execution Time ◽  
Constraint Logic Programming ◽  
Complete Problem ◽  
Maximal Amount ◽  
Np Complete ◽  
General Goal ◽  
Shared Structure

AbstractAnti-unification refers to the process of generalizing two (or more) goals into a single, more general, goal that captures some of the structure that is common to all initial goals. In general one is typically interested in computing what is often called a most specific generalization, that is a generalization that captures a maximal amount of shared structure. In this work we address the problem of anti-unification in CLP, where goals can be seen as unordered sets of atoms and/or constraints. We show that while the concept of a most specific generalization can easily be defined in this context, computing it becomes an NP-complete problem. We subsequently introduce a generalization algorithm that computes a well-defined abstraction whose computation can be bound to a polynomial execution time. Initial experiments show that even a naive implementation of our algorithm produces acceptable generalizations in an efficient way.

scholarly journals Hybrid Scheduling Strategy in Cloud Computing based on Optimization Algorithms

2021 ◽  
Vol 4 (1) ◽  
pp. 226-234
Author(s):  
Komal . ◽  
Gaurav Goel ◽  
Milanpreet Kaur
Keyword(s):  
Cloud Computing ◽  
Execution Time ◽  
Cloud Service ◽  
Previous Method ◽  
Optimization Techniques ◽  
Energy Usage ◽  
Complete Problem ◽  
Mutation Operators ◽  
Np Complete ◽  
Time And Energy

As a platform for offering on-demand services, cloud computing has increased in relevance and appeal. It has a pay-per-use model for its services. A cloud service provider's primary goal is to efficiently use resources by reducing execution time, cost, and other factors while increasing profit. As a result, effective scheduling algorithms remain a key issue in cloud computing, and this topic is categorized as an NP-complete problem. Researchers previously proposed several optimization techniques to address the NP-complete problem, but more work is needed in this area. This paper provides an overview of strategy for successful task scheduling based on a hybrid heuristic approach for both regular and larger workloads. The previous method handles the jobs adequately, but its performance degrades as the task size becomes larger. The proposed optimum scheduling method employs two distinct techniques to select the suitable VM for the specified job. To begin, it enhances the LJFP method by employing OSIG, an upgraded version of the Genetic Algorithm, to choose solutions with improved fitness factors, crossover, and mutation operators. This selection returns the best machines, and PSO then chooses one for a specific job. The appropriate machine is chosen depending on several factors, including the expected execution time, current load, and energy usage. The proposed algorithm's performance is assessed using two distinct cloud scenarios with various VMs and tasks, and overall execution time and energy usage are calculated. The proposed algorithm outperforms existing techniques in terms of energy and average execution time usage in both scenarios.

scholarly journals Statistical mechanics of an NP-complete problem: subset sum

2001 ◽  
Vol 34 (44) ◽  
pp. 9555-9567 ◽  
Author(s):  
Tomohiro Sasamoto ◽  
Taro Toyoizumi ◽  
Hidetoshi Nishimori
Keyword(s):  
Statistical Mechanics ◽  
Complete Problem ◽  
Subset Sum ◽  
Np Complete

scholarly journals Consecutive Colouring of Oriented Graphs

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
Marta Borowiecka-Olszewska ◽  
Ewa Drgas-Burchardt ◽  
Nahid Yelene Javier-Nol ◽  
Rita Zuazua
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Bipartite Graphs ◽  
Complete Graphs ◽  
Oriented Graphs ◽  
Complete Problem ◽  
Np Complete

AbstractWe consider arc colourings of oriented graphs such that for each vertex the colours of all out-arcs incident with the vertex and the colours of all in-arcs incident with the vertex form intervals. We prove that the existence of such a colouring is an NP-complete problem. We give the solution of the problem for r-regular oriented graphs, transitive tournaments, oriented graphs with small maximum degree, oriented graphs with small order and some other classes of oriented graphs. We state the conjecture that for each graph there exists a consecutive colourable orientation and confirm the conjecture for complete graphs, 2-degenerate graphs, planar graphs with girth at least 8, and bipartite graphs with arboricity at most two that include all planar bipartite graphs. Additionally, we prove that the conjecture is true for all perfect consecutively colourable graphs and for all forbidden graphs for the class of perfect consecutively colourable graphs.

scholarly journals Analysis of Decision Tree Induction Algorithms

2019 ◽  
Vol 8 (11) ◽  
pp. e298111473
Author(s):  
Hugo Kenji Rodrigues Okada ◽  
Andre Ricardo Nascimento das Neves ◽  
Ricardo Shitsuka
Keyword(s):  
Machine Learning ◽  
Decision Tree ◽  
Decision Trees ◽  
Quantitative Study ◽  
Data Structures ◽  
Execution Time ◽  
Supervised Machine Learning ◽  
Decision Tree Induction ◽  
Classification And Regression ◽  
Cart Algorithm

Decision trees are data structures or computational methods that enable nonparametric supervised machine learning and are used in classification and regression tasks. The aim of this paper is to present a comparison between the decision tree induction algorithms C4.5 and CART. A quantitative study is performed in which the two methods are compared by analyzing the following aspects: operation and complexity. The experiments presented practically equal hit percentages in the execution time for tree induction, however, the CART algorithm was approximately 46.24% slower than C4.5 and was considered to be more effective.

Dealing with Hardness

2017 ◽  
Author(s):  
Lance Fortnow
Keyword(s):  
Brute Force ◽  
Complete Problem ◽  
Hard Problems ◽  
Np Complete ◽  
Np Problems ◽  
Single Technique

This chapter demonstrates several approaches for dealing with hard problems. These approaches include brute force, heuristics, and approximation. Typically, no single technique will suffice to handle the difficult NP problems one needs to solve. For moderate-sized problems one can search over all possible solutions with the very fast computers available today. One can use algorithms that might not work for every problem but do work for many of the problems one cares about. Other algorithms may not find the best possible solution but still a solution that's good enough. Other times one just cannot get a solution for an NP-complete problem. One has to try to solve a different problem or just give up.

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