Chio’s-like Method for Calculating the Rectangular (non-square) Determinants: Computer Algorithm  Interpretation and Comparison

In this paper, we present an approach for the calculation of rectangular determinants, where in addition to the mathematical formula, we also provide a computer algorithm for their calculation. Firstly, we present a method similar to Sarrus method for calculating the rectangular determinant of the order 2 × 3. Secondly, we present an approach for calculating the rectangular determinants of order m ×n by adding a row with all elements equal to one (1) in any row, as well as an application of Chio’s rule for calculating the rectangular determinants. Thirdly, we find the time complexity and comparison of the computer execution time of calculation of the rectangular determinant based on the presented algorithms and comparing them with the algorithm based on the Laplace method.

Download Full-text

Greedy Selection of Materialized Views

International Journal of Computer and Communication Technology ◽

10.47893/ijcct.2010.1006 ◽

2010 ◽

pp. 47-58

Author(s):

T.V. Vijay Kumar ◽

Aloke Ghoshal

Keyword(s):

Polynomial Time ◽

Execution Time ◽

Time Complexity ◽

Materialized Views ◽

View Selection ◽

Multidimensional Lattice ◽

View Materialization ◽

Good Set ◽

Selection Of

Greedy based approach for view selection at each step selects a beneficial view that fits within the space available for view materialization. Most of these approaches are focused around the HRU algorithm, which uses a multidimensional lattice framework to determine a good set of views to materialize. The HRU algorithm exhibits high run time complexity as the number of possible views is exponential with respect to the number of dimensions. The PGA algorithm provides a scalable solution to this problem by selecting views for materialization in polynomial time relative to the number of dimensions. This paper compares the HRU and the PGA algorithm. It was experimentally deduced that the PGA algorithm, in comparison with the HRU algorithm, achieves an improved execution time with lowered memory and CPU usages. The HRU algorithm has an edge over the PGA algorithm on the quality of the views selected for materialization.

Download Full-text

Parallel Random Walk for P/G Analysis

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.427-429.2787 ◽

2013 ◽

Vol 427-429 ◽

pp. 2787-2790

Author(s):

Jun Guo ◽

Cang Song Zhang ◽

Jiao Cui

Keyword(s):

Parallel Computing ◽

Random Walk ◽

Execution Time ◽

Time Complexity ◽

Formal Model ◽

Power Grid ◽

Random Walk Algorithm ◽

Main Factors ◽

Parallel Features ◽

Walk Algorithm

This paper introduced parallel computing techniques to improve random walk algorithm. The random walk problem was firstly explained by a formal model. And then, the parallel features of random walk algorithm were discussed in detail. A parallel random walk algorithm was proposed and applied to analyze the VLSI power grid. The time complexity and the main factors impacting on the execution time of algorithm were analyzed carefully. The experimental results proved that the parallel computing techniques could improve random walk algorithm effectively.

Download Full-text

THE TIME COMPLEXITY OF SCHEDULING INTERVAL ORDERS WITH COMMUNICATION IS POLYNOMIAL

Parallel Processing Letters ◽

10.1142/s0129626493000083 ◽

1993 ◽

Vol 03 (01) ◽

pp. 53-58 ◽

Cited By ~ 12

Author(s):

HESHAM H. ALI ◽

HESHAM EL-REWINI

Keyword(s):

Execution Time ◽

Time Complexity ◽

Linear Time ◽

Communication Cost ◽

Interval Order ◽

Task Graph ◽

Scheduling Problem ◽

Interval Orders ◽

Schedule Length ◽

Np Complete

Papadimitrjou and Yannakakis showed that unit execution time tasks in interval orders can be scheduled in linear time on N processors when communication cost is ignored. The objective function was to minimize the schedule length. They have also shown that the generalization of this problem to arbitrary execution times is NP- complete . In this paper, we study the problem of scheduling task graphs with communication on N processors when the task graph is an interval order. We prove that this scheduling problem can be solved in polynomial time when the execution cost of the system tasks is identical and equal to the communication cost between any pair of processors. We introduce an algorithm of O(Ne) to minimize the schedule length, where e is the number of arcs in the interval order.

Download Full-text

Automatic Synthesis of Smart Table Constraints by Abstraction of Table Constraints

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2017/95 ◽

2017 ◽

Author(s):

Baudouin Le Charlier ◽

Minh Thanh Khong ◽

Christophe Lecoutre ◽

Yves Deville

Keyword(s):

Simple Form ◽

Execution Time ◽

Time Complexity ◽

State Of The Art ◽

Experimental Results ◽

Global Constraints ◽

Automatic Synthesis ◽

Compression Efficiency ◽

Filtering Algorithms ◽

Input Table

The smart table constraint represents a powerful modeling tool that has been recently introduced. This constraint allows the user to represent compactly a number of well-known (global) constraints and more generally any arbitrarily structured constraints, especially when disjunction is at stake. In many problems, some constraints are given under the basic and simple form of tables explicitly listing the allowed combinations of values. In this paper, we propose an algorithm to convert automatically any (ordinary) table into a compact smart table. Its theoretical time complexity is shown to be quadratic in the size of the input table. Experimental results demonstrate its compression efficiency on many constraint cases while showing its reasonable execution time. It is then shown that using filtering algorithms on the resulting smart table is more efficient than using state of the art filtering algorithms on the initial table.

Download Full-text

Reduction of programs execution time for tasks related to sequences or matrices

SHS Web of Conferences ◽

10.1051/shsconf/20207504019 ◽

2020 ◽

Vol 75 ◽

pp. 04019

Author(s):

Oleksandr Mitsa ◽

Yurii Horoshko ◽

Serhii Vapnichnyi

Keyword(s):

Computer Science ◽

Execution Time ◽

Time Complexity ◽

Matrix Multiplication ◽

Matrix Form ◽

The Third

The article discusses three approaches to reducing runtime of the programs, which are solutions of Olympiad tasks on computer science, related to sequences or matrices. The first approach is based on the representation of some sequences in matrix form and then the program of calculating the members of the sequence will have asymptotics equal to the time complexity of the exponentiation algorithm and will be O(log (n)). The second approach is to upgrade the known code to obtain significant reduction of the program runtime. This approach is very important to know for scientists who write code for scientific researches and are faced with matrix multiplication operations. The third approach is based on reducing time complexity by search for regularities; the author's task is presented and this approach is used to solve it.

Download Full-text

On the Efficiency of Querying and Storing RDF Documents

Advances in Data Mining and Database Management - Graph Data Management ◽

10.4018/978-1-61350-053-8.ch016 ◽

2011 ◽

pp. 354-385

Author(s):

Maria-Esther Vidal ◽

Amadís Martínez ◽

Edna Ruckhaus ◽

Tomas Lampo ◽

Javier Sierra

Keyword(s):

Query Processing ◽

Execution Time ◽

Time Complexity ◽

Low Cost ◽

Data Access ◽

Optimization Techniques ◽

Experimental Results ◽

Access Time ◽

Alternative Representation ◽

Rdf Data

In the context of the Semantic Web, different approaches have been defined to represent RDF documents, and the selected representation affects storage and time complexity of the RDF data recovery and query processing tasks. This chapter addresses the problem of efficiently querying and storing RDF documents, and presents an alternative representation of RDF data, Bhyper, which is based on hypergraphs. Additionally, access and optimization techniques to efficiently execute queries with low cost, are defined on top of this hypergraph based representation. The chapter’s authors have empirically studied the performance of the Bhyper based techniques, and their experimental results show that the proposed hypergraph based formalization reduces the RDF data access time as well as the space needed to store the Bhyper structures, while the query execution time of state-the-of-art RDF engines can be sped up by up to two orders of magnitude.

Download Full-text

DYNAMIC REDUCTS GENERATION USING CASCADING HASHES

International Journal of Foundations of Computer Science ◽

10.1142/s0129054114500117 ◽

2014 ◽

Vol 25 (02) ◽

pp. 219-246 ◽

Cited By ~ 1

Author(s):

PAI-CHOU WANG

Keyword(s):

Rough Set ◽

Execution Time ◽

Random Sampling ◽

Hash Function ◽

Time Complexity ◽

Decision Table ◽

Hash Tables ◽

Dynamic Reduct ◽

Original Classification

Reducts preserve original classification properties using minimal number of attributes in a table. Dynamic reducts are the most stable reducts in the process of random sampling of original decision table, and they are proposed to classify unseen cases. Classical reduct generation methods can be applied to compute dynamic reducts but the time complexity of computing dynamic reducts are rarely discussed. This paper proposes a cascading hash function, and dynamic reduct can be derived in O(m2n) time with O(mn) space where m and n are total number of attributes and total number of instances of the table. Core of dynamic reducts is also discussed, and the computation of core of dynamic reducts takes O(mn) time with O(mn) space. Sixteen UCI datasets are applied to compute (F, ε)-dynamic reducts for ε = 1, and results are compared to Rough Set Exploration System (RSES). Results show the execution time on generating dynamic reducts using cascading hash tables is faster than RSES up to 1700 times. Besides the efficiency issue of the algorithms, our algorithms are also very easy to implement and applicable to any system.

Download Full-text

A new algorithm for enumerating all possible Sudoku squares

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830916500269 ◽

2016 ◽

Vol 08 (02) ◽

pp. 1650026 ◽

Cited By ~ 1

Author(s):

Pallavi Mishra ◽

D. K. Gupta ◽

Rakesh P. Badoni

Keyword(s):

Positive Integer ◽

Computational Efficiency ◽

Time Complexity ◽

Worst Case ◽

Mathematical Formula ◽

Generation Algorithm ◽

Permutation Matrices ◽

Simple Rules ◽

One To One ◽

Permutation Generation

Sudoku is an interesting number placement puzzle with some simple rules. For some positive integer [Formula: see text], the puzzle involves an [Formula: see text] grid partitioned into [Formula: see text] distinct blocks each of size [Formula: see text] such that the integers [Formula: see text] through [Formula: see text] appear exactly once in each row, each column and each block of the grid. Often some static numbers known as givens are placed according to the difficulty rating in the puzzle and then the rule is to place the numbers from [Formula: see text] to [Formula: see text] in the partially filled grid such that the conditions of the puzzle are satisfied. The aim of this paper is to propose a new algorithm for enumerating all possible Sudoku squares of size [Formula: see text]. It is based on the concepts of permutations derived from [Formula: see text] S-permutation matrices termed as S-permutations. There is a one-to-one correspondence between Sudoku squares and the set of those S-permutation matrices which are mutually disjoint to each other. The proposed algorithm uses the set of all S-permutations generated by some permutation generation algorithm as input and then enumerates all the subsets of cardinality [Formula: see text] of all S-permutations which are mutually disjoint to each other. The correctness of the algorithm is established. Its worst-case time complexity is O[Formula: see text], where [Formula: see text]. A mathematical formula involving the total number of the sets of [Formula: see text] mutually disjoint S-permutations is also derived. Experimentally, the proposed algorithm is verified for the Sudoku squares of size [Formula: see text]. It is observed that our algorithm is more systematic and better in terms of computational efficiency.

Download Full-text