scholarly journals The Good Old Davis-Putnam Procedure Helps Counting Models

1999 ◽  
Vol 10 ◽  
pp. 457-477 ◽  
Author(s):  
E. Birnbaum ◽  
E. L. Lozinskii
Keyword(s):  
Present Knowledge ◽  
Worst Case ◽  
Running Time ◽  
Exact Number ◽  
Average Running Time ◽  
Practical Performance ◽  
Series Of Experiments ◽  
Case Based ◽  
Cnf Formulas ◽  
Dnf Formula

As was shown recently, many important AI problems require counting the number of models of propositional formulas. The problem of counting models of such formulas is, according to present knowledge, computationally intractable in a worst case. Based on the Davis-Putnam procedure, we present an algorithm, CDP, that computes the exact number of models of a propositional CNF or DNF formula F. Let m and n be the number of clauses and variables of F, respectively, and let p denote the probability that a literal l of F occurs in a clause C of F, then the average running time of CDP is shown to be O(nm^d), where d=-1/log(1-p). The practical performance of CDP has been estimated in a series of experiments on a wide variety of CNF formulas.

Constructing Delaunay Triangulations by Merging Buckets in Quad Tree Order

1988 ◽  
Vol 11 (3) ◽  
pp. 275-288
Author(s):  
Jyrki Katajainen ◽  
Markku Koppinen
Keyword(s):  
Delaunay Triangulation ◽  
Slight Modification ◽  
Divide And Conquer ◽  
Worst Case ◽  
Delaunay Triangulations ◽  
Running Time ◽  
Expected Time ◽  
Divide And Conquer Algorithm ◽  
Quad Tree ◽  
Average Running Time

Recently Rex Dwyer [D87] presented an algorithm which constructs a Delaunay triangulation for a planar set of N sites in O(N log log N) expected time and O(N log N) worst-case time. We show that a slight modification of his algorithm preserves the worst-case running time, but has only O(N) average running time. The methcxl is a hybrid which combines the cell technique with the divide-and-conquer algorithm of Guibas & Stolfi [GS85]. First a square grid of size about N by N is placed on the set of sites. The grid forms about N cells (buckets), each of which is implemented as a list of the sites which fall into the corresponding square of the grid. A Delaunay triangulation of the generally rather few sites within each cell is constructed with the Guibas & Stolfi algorithm. Then the triangulations are merged, four by four, in a quadtree-like order.

scholarly journals A Comparative Study among New Hybrid Root Finding Algorithms and Traditional Methods

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1306
Author(s):  
Elsayed Badr ◽  
Sultan Almotairi ◽  
Abdallah El Ghamry
Keyword(s):  
Comparative Study ◽  
Numerical Results ◽  
Traditional Methods ◽  
Running Time ◽  
Root Finding ◽  
Average Running Time ◽  
False Position ◽  
Newton Raphson ◽  
Number Of Iterations

In this paper, we propose a novel blended algorithm that has the advantages of the trisection method and the false position method. Numerical results indicate that the proposed algorithm outperforms the secant, the trisection, the Newton–Raphson, the bisection and the regula falsi methods, as well as the hybrid of the last two methods proposed by Sabharwal, with regard to the number of iterations and the average running time.

scholarly journals On the Average Running Time of Odd–Even Merge Sort

1997 ◽  
Vol 22 (2) ◽  
pp. 329-346 ◽  
Author(s):  
Christine Rüb
Keyword(s):  
Running Time ◽  
Average Running Time ◽  
Merge Sort

scholarly journals On domain-partitioning induction criteria: worst-case bounds for the worst-case based

2004 ◽  
Vol 321 (2-3) ◽  
pp. 371-382 ◽  
Author(s):  
Richard Nock ◽  
Frank Nielsen
Keyword(s):  
Worst Case ◽  
Domain Partitioning ◽  
Case Based

scholarly journals Optimal Purely Functional Priority Queues

1996 ◽  
Vol 3 (37) ◽  
Author(s):  
Gerth Stølting Brodal ◽  
Chris Okasaki
Keyword(s):  
Data Structure ◽  
Higher Order ◽  
Priority Queues ◽  
Worst Case ◽  
Minimum Element ◽  
Asymptotically Optimal ◽  
Running Time ◽  
Recursive Structures ◽  
Functional Setting

Brodal recently introduced the first implementation of imperative priority queues to support findMin, insert, and meld in O(1) worst-case time, and deleteMin in O(log n) worst-case time. These bounds are asymptotically optimal among all comparison-based priority queues. In this paper, we adapt<br />Brodal's data structure to a purely functional setting. In doing so, we both simplify the data structure and clarify its relationship to the binomial queues of Vuillemin, which support all four operations in O(log n) time. Specifically, we derive our implementation from binomial queues in three steps: first, we reduce the running time of insert to O(1) by eliminating the possibility of cascading links; second, we reduce the running time of findMin to O(1) by adding a global root to hold the minimum element; and finally, we reduce the running time of meld to O(1) by allowing priority queues to contain other<br />priority queues. Each of these steps is expressed using ML-style functors. The last transformation, known as data-structural bootstrapping, is an interesting<br />application of higher-order functors and recursive structures.

scholarly journals Research on Intelligent Solution of Service Industry Supply Chain Network Optimization Based on Genetic Algorithm

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Yixin Zhou ◽  
Zhen Guo
Keyword(s):  
Genetic Algorithm ◽  
Supply Chain ◽  
Network Optimization ◽  
Service Industry ◽  
User Behavior ◽  
Service Level ◽  
Supply Chain Network ◽  
Supply Network ◽  
Running Time ◽  
Average Running Time

With the advent of the era of big data (BD), people’’s living standards and lifestyle have been greatly changed, and people’s requirements for the service level of the service industry are becoming higher and higher. The personalized needs of customers and private customization have become the hot issues of current research. The service industry is the core enterprise of the service industry. Optimizing the service industry supply network and reasonably allocating the tasks are the focus of the research at home and abroad. Under the background of BD, this paper takes the optimization of service industry supply network as the research object and studies the task allocation optimization of service industry supply network based on the analysis of customers’ personalized demand and user behavior. This paper optimizes the supply chain network of service industry based on genetic algorithm (GA), designs genetic operator, effectively avoids the premature of the algorithm, and improves the operation efficiency of the algorithm. The experimental results show that when m = 8 and n = 40, the average running time of the improved GA is 54.1 s. The network optimization running time of the algorithm used in this paper is very fast, and the stability is also higher.

The Research on the Osmotic Stress Gene Mining Model Based on the Arabidopsis Genome

2019 ◽  
Vol 12 (1) ◽  
pp. 117-132
Author(s):  
Xiao Yu ◽  
Xiang Li ◽  
Huihui Deng ◽  
Yuchen Tang ◽  
Zhepeng Hou ◽  
...  
Keyword(s):  
Experimental Data ◽  
Osmotic Stress ◽  
High Speed ◽  
Promoter Sequence ◽  
P Value ◽  
Running Time ◽  
Cis Element ◽  
Technology Roadmap ◽  
Gene Mining ◽  
Average Running Time

In the field of the bioinformatics, during osmotic stress response genes mining processing, it is also very crucial to verify experimental data obtained in the course of complex experiments by using the computer. Aim of this paper is taking Arabidopsis thaliana as the experimental crop, designing technology roadmap, taking advantage of the skills of function and programming, then designing algorithms. After using the program to predict the transcription start point, the promoter sequence is extracted and simplified. In addition, different alignment methods are classified. Then, comparing the promoter sequence with the cis-element and using the formula for further processing. Finally, get the probability P value, which provide further help to experts and scholars on the basis of probability values to determine the correlation between the osmotic stress. The experimental data source of chromosomal sequences is received from Genbank database files, and cis-element sequence that associated with osmotic stress is collected from TRANSFAC and TRRD database. From this, the authors not only used the Arabidopsis promoter as the experimental data, but also use a variety of eukaryotic promoters include promoters GhNHX1 rice, cotton OsNHX1 promoter, as a comparison. Wherein the data obtained in the biological laboratory, which in the course of running the program, 70% have been verified. P value close to 0.8, this article will be treated as the promoter contains osmotic stress cis-elements, the expression of gene induced by osmotic stress. For thaliana, cotton and rice, programs running average time was 51s, 72s and 114s. Through the use of some commonly used bioinformatics gene mining algorithms, MEME algorithm and BioProspector algorithm for the same data have been processed, the average running time of the system is increasing with the increase of data. Running time of MEME algorithm increases from 60s to reach 198s, BioProspector algorithm increases from 45s to 150s model process used herein were 50s, 75s, 110s, 135s. At the same time, the authors can see in the three algorithms, the model algorithm used herein with respect to the first two more optimized. To ensure the accuracy rate, meanwhile has high speed and stabilization of higher.

scholarly journals Average running time analysis of an algorithm to calculate the size of the union of Cartesian products

2003 ◽  
Vol 273 (1-3) ◽  
pp. 211-220
Author(s):  
Susumu Suzuki ◽  
Toshihide Ibaraki
Keyword(s):  
Time Analysis ◽  
Cartesian Products ◽  
Running Time ◽  
Running Time Analysis ◽  
Average Running Time
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