scholarly journals Restrictions and Generalizations on Comma-Free Codes

10.37236/114 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Alexander L. Churchill
Keyword(s):  
Word Length ◽  
Coding Theory ◽  
Correspondence Problem ◽  
Major Difficulty ◽  
Alphabet Size ◽  
New Class ◽  
Np Complete

A significant sector of coding theory is that of comma-free coding; that is, codes which can be received without the need of a letter used for word separation. The major difficulty is in finding bounds on the maximum number of comma-free words which can inhabit a dictionary. We introduce a new class called a self-reflective comma-free dictionary and prove a series of bounds on the size of such a dictionary based upon word length and alphabet size. We also introduce other new classes such as self-swappable comma-free codes and comma-free codes in q dimensions and prove preliminary bounds for these classes. Finally, we discuss the implications and applications of combining these original concepts, including their implications for the NP-complete Post Correspondence Problem.

scholarly journals Discovering the maximum k-clique on social networks using bat optimization algorithm

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Akram Khodadadi ◽  
Shahram Saeidi
Keyword(s):  
Genetic Algorithm ◽  
Social Networks ◽  
Social Network ◽  
Coding Theory ◽  
Evaluation Criteria ◽  
Convergence Speed ◽  
Optimization Approach ◽  
Computational Results ◽  
Complete Subgraph ◽  
Np Complete

AbstractThe k-clique problem is identifying the largest complete subgraph of size k on a network, and it has many applications in Social Network Analysis (SNA), coding theory, geometry, etc. Due to the NP-Complete nature of the problem, the meta-heuristic approaches have raised the interest of the researchers and some algorithms are developed. In this paper, a new algorithm based on the Bat optimization approach is developed for finding the maximum k-clique on a social network to increase the convergence speed and evaluation criteria such as Precision, Recall, and F1-score. The proposed algorithm is simulated in Matlab® software over Dolphin social network and DIMACS dataset for k = 3, 4, 5. The computational results show that the convergence speed on the former dataset is increased in comparison with the Genetic Algorithm (GA) and Ant Colony Optimization (ACO) approaches. Besides, the evaluation criteria are also modified on the latter dataset and the F1-score is obtained as 100% for k = 5.

Priority-based task scheduling on heterogeneous resources in the Expert Cloud

Kybernetes ◽  
2015 ◽  
Vol 44 (10) ◽  
pp. 1455-1471 ◽  
Author(s):  
Mehran Ashouraie ◽  
Nima Jafari Navimipour
Keyword(s):  
Genetic Algorithm ◽  
Task Scheduling ◽  
Design Methodology ◽  
Fitness Function ◽  
Content Type ◽  
Cloud Systems ◽  
New Class ◽  
Complete Problems ◽  
Np Complete ◽  
Real World Situation

Purpose – Expert Cloud as a new class of Cloud systems provides the knowledge and skills of human resources (HRs) as a service using Cloud concepts. Task scheduling in the Expert Cloud is a vital part that assigns tasks to suitable resources for execution. The purpose of this paper is to propose a method based on genetic algorithm to consider the priority of arriving tasks and the heterogeneity of HRs. Also, to simulate a real world situation, the authors consider the human-based features of resources like trust, reputation and etc. Design/methodology/approach – As it is NP-Complete to schedule tasks to obtain the minimum makespan and the success of genetic algorithm in optimization and NP-Complete problems, the authors used a genetic algorithm to schedule the tasks on HRs in the Expert Cloud. In this method, chromosome or candidate solutions are represented by a vector; fitness function is calculated based on several factors; one point cross-over and swap mutation are also used. Findings – The obtained results demonstrated the efficiency of the proposed algorithm in terms of time complexity, task fail rate and HRs utilization. Originality/value – In this paper the task scheduling issue in the Expert Cloud and improving pervious algorithm are pointed out and the approach to resolve the problem is applied into a practical example.

Review on Multiobjective Task Scheduling in Cloud Computing using Nature Inspired Algorithms

2018 ◽  
Vol 6 (8) ◽  
pp. 282
Author(s):  
Shikha Chaudhary ◽  
Saroj Hiranwal ◽  
C. P. Gupta
Keyword(s):  
Cloud Computing ◽  
Optimal Solution ◽  
Computing System ◽  
Ant Colony Optimization Algorithm ◽  
New Class ◽  
Complete Problem ◽  
Nature Inspired Algorithm ◽  
Cloud Computing System ◽  
Np Complete ◽  
Nature Inspired Algorithms

In cloud computing huge pool of resources are available and shared through internet. The scheduling is a core technique which determines the performance of a cloud computing system. The goal of scheduling is to allocate task to appropriate machine to achieve one or more QOS. To find the suitable resource among pool of resources to achieve the goal is an NP Complete problem. A new class of algorithm called nature inspired algorithm came into existence to find optimal solution.  In this paper we provide a survey as well as a comparative analysis of various existing nature inspired scheduling algorithms which are based on genetic algorithm and ant colony optimization algorithm. 

Exploiting the Inter-Domain Hierarchy for the QoS Network Management

2010 ◽  
pp. 239-255
Author(s):  
Marc-Antoine Weisser ◽  
Joanna Tomasik ◽  
Dominique Barth
Keyword(s):  
Quality Parameters ◽  
Directed Acyclic Graphs ◽  
The Internet ◽  
Steiner Problem ◽  
Major Difficulty ◽  
Multiple Networks ◽  
Acyclic Graphs ◽  
The Hierarchical Structure ◽  
Bgp Routing ◽  
Np Complete

The Internet is an interconnection of multiple networks called domains. Inter-domain routing is ensured by BGP which preserves each domain’s independence and announces routes arbitrarily chosen by domains. BGP messages carry no information concerning quality parameters of announced routes. The authors’ goal is to provide domains with information regarding the congestion state of other domains without any changes in BGP. A domain, which is aware of heavily congested domains, can choose a bypass instead of a route exhibiting possible problems with QoS satisfaction. They propose a mechanism which sends alert messages in order to notify domains about the congestion state of other domains. The major difficulty consists in avoiding flooding the Internet with signaling messages. The authors’ solution limits the number of alerts by taking advantage of the hierarchical structure of the Internet set by P2C and P2P relationships. Their algorithm is distributed and heuristic because it is a solution to an NP-complete and inapproximable problem. They prove these properties by reducing the Steiner problem in directed acyclic graphs to our problem of alert diffusion. The simulations show that our mechanism significantly diminishes the number of unavailable domains and routes compared to those obtained with BGP routing and with a theoretical centralized mechanism.

Find balance, as in coding theory

2020 ◽  
pp. 211-216
Author(s):  
Susan D'Agostino
Keyword(s):  
Error Detection ◽  
Word Length ◽  
Coding Theory ◽  
Code Word ◽  
Transmission Time ◽  
Optimal Codes ◽  
Mathematics Students ◽  
The Right ◽  
Undesirable Outcome ◽  
Just Right

“Find balance, as in coding theory” explains how mathematicians construct codes to transmit messages as accurately and efficiently as possible. Since “noise” may corrupt messages during transmission, a good code repeats some of the information in a sent message so that errors due to noise in the received message may be detected and (ideally) corrected. However, too much repetition increases not only the code word length but the transmission time—an undesirable outcome. Mathematician Claude Shannon proved that “optimal” codes with just the right balance between repetition in transmission and error detection exist. Mathematics students and enthusiasts are encouraged to find a balance that is just right between repetition and forward momentum in mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem concerning book International Standard Book Numbers (ISBNs). A solution is provided.

(R, S)-Norm Information Measure and A Relation Between Coding and Questionnaire Theory

2016 ◽  
Vol 23 (03) ◽  
pp. 1650015 ◽  
Author(s):  
Rajesh Joshi ◽  
Satish Kumar
Keyword(s):  
Lower Bound ◽  
Word Length ◽  
Coding Theory ◽  
Code Word ◽  
Information Measure ◽  
The Relationship

In this paper, we introduce a quantity which is called (R, S)-norm entropy and discuss some of its major properties in comparison with Shannon’s and other entropies known in the literature. Further, we give an application of (R, S)-norm entropy in coding theory and a coding theorem analogous to the ordinary coding theorem for a noiseless channel. The theorem states that the proposed entropy is the lower bound of mean code word length. Further, we give an application of (R, S)-norm entropy and noiseless coding theorem in questionnaire theory. We show that the relationship between noiseless coding theorem and questionnaire theory through a charging scheme based on the resolution of questions and lower bound on the measure of the charge can also be obtained.

High rates of Fibonacci polynomials coding theory

2014 ◽  
Vol 06 (04) ◽  
pp. 1450053
Author(s):  
Bandhu Prasad
Keyword(s):  
Coding Theory ◽  
Fibonacci Polynomials ◽  
New Class ◽  
Matrix Formula ◽  
Fibonacci Polynomial ◽  
Square Matrix

In this paper, a new class of square matrix [Formula: see text] of order pm is introduced, where (p = 3, 4, 5, …), (m = 1, 2, 3, …) and for integers n, x ≥ 1. Fibonacci polynomial coding and decoding methods are followed from [Formula: see text] matrix and high code rates are obtained.

scholarly journals Counting Finite Languages by Total Word Length

Integers ◽  
2011 ◽  
Vol 11 (6) ◽  
Author(s):  
Stefan Gerhold
Keyword(s):  
Explicit Expression ◽  
Generating Function ◽  
Word Length ◽  
Finite Alphabet ◽  
Alphabet Size ◽  
Total Length ◽  
Large Alphabet ◽  
Finite Language

AbstractWe investigate the number of sets of words that can be formed from a finite alphabet, counted by the total length of the words in the set. An explicit expression for the counting sequence is derived from the generating function, and asymptotics for large alphabet size and large total word length are discussed. Moreover, we derive a Gaussian limit law for the number of words in a random finite language.

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