scholarly journals Edge coloring of graphs, uses, limitation, complexity

2016 ◽  
Vol 8 (1) ◽  
pp. 63-81
Author(s):  
Sándor Szabó ◽  
Bogdán Zaválnij
Keyword(s):  
Upper Bound ◽  
Search Algorithm ◽  
Edge Coloring ◽  
Clique Number ◽  
Optimal Number ◽  
Np Hard ◽  
Main Motivation

Abstract The known fact that coloring of the nodes of a graph improves the performance of practical clique search algorithm is the main motivation of this paper. We will describe a number of ways in which an edge coloring scheme proposed in [8] can be used in clique search. The edge coloring provides an upper bound for the clique number. This estimate has a limitation. It will be shown that the gap between the clique number and the upper bound can be arbitrarily large. Finally, it will be shown that to determine the optimal number of colors in an edge coloring is NP-hard.

scholarly journals Rainbow Connectivity Using a Rank Genetic Algorithm: Moore Cages with Girth Six

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
J. Cervantes-Ojeda ◽  
M. Gómez-Fuentes ◽  
D. González-Moreno ◽  
M. Olsen
Keyword(s):  
Genetic Algorithm ◽  
Upper Bound ◽  
Connected Graph ◽  
Edge Coloring ◽  
Np Hard ◽  
The Family ◽  
Minimum Number ◽  
The One ◽  
Vertex Disjoint ◽  
Rainbow Coloring

Arainbowt-coloringof at-connected graphGis an edge coloring such that for any two distinct verticesuandvofGthere are at leasttinternally vertex-disjoint rainbow(u,v)-paths. In this work, we apply a Rank Genetic Algorithm to search for rainbowt-colorings of the family of Moore cages with girth six(t;6)-cages. We found that an upper bound in the number of colors needed to produce a rainbow 4-coloring of a(4;6)-cage is 7, improving the one currently known, which is 13. The computation of the minimum number of colors of a rainbow coloring is known to be NP-Hard and the Rank Genetic Algorithm showed good behavior finding rainbowt-colorings with a small number of colors.

A New Solution Seed for Job Shop Scheduling Problem

2011 ◽  
Vol 110-116 ◽  
pp. 3899-3905
Author(s):  
Parviz Fattahi ◽  
Mojdeh Shirazi Manesh ◽  
Abdolreza Roshani
Keyword(s):  
Tabu Search ◽  
Large Scale ◽  
Production Management ◽  
Job Shop ◽  
Job Shop Scheduling ◽  
Search Algorithm ◽  
Tabu Search Algorithm ◽  
Np Hard ◽  
Shop Scheduling ◽  
Large Scale Problems

Scheduling for job shop is very important in both fields of production management and combinatorial optimization. Since the problem is well known as NP-Hard class, many metaheuristic approaches are developed to solve the medium and large scale problems. One of the main elements of these metaheuristics is the solution seed structure. Solution seed represent the coding structure of real solution. In this paper, a new solution seed for job shop scheduling is presented. This solution seed is compared with a famous solution seed presented for the job shop scheduling. Since the problem is well known as NP-Hard class, a Tabu search algorithm is developed to solve large scale problems. The proposed solution seed are examined using an example and tabu search algorithm.

scholarly journals ON SPANNERS OF GEOMETRIC GRAPHS

2009 ◽  
Vol 20 (01) ◽  
pp. 135-149 ◽  
Author(s):  
JOACHIM GUDMUNDSSON ◽  
MICHIEL SMID
Keyword(s):  
Real Number ◽  
Upper Bound ◽  
Weighted Graph ◽  
Geometric Graph ◽  
Geometric Graphs ◽  
Np Hard ◽  
Minimum Number ◽  
Np Hardness

Given a connected geometric graph G, we consider the problem of constructing a t-spanner of G having the minimum number of edges. We prove that for every real number t with [Formula: see text], there exists a connected geometric graph G with n vertices, such that every t-spanner of G contains Ω(n1+1/t) edges. This bound almost matches the known upper bound, which states that every connected weighted graph with n vertices contains a t-spanner with O(n1+2/(t-1)) edges. We also prove that the problem of deciding whether a given geometric graph contains a t-spanner with at most K edges is NP-hard. Previously, this NP-hardness result was only known for non-geometric graphs.

Automatic Data Clustering Using Parameter Adaptive Harmony Search Algorithm and Its Application to Image Segmentation

2016 ◽  
Vol 25 (4) ◽  
pp. 595-610 ◽  
Author(s):  
Vijay Kumar ◽  
Jitender Kumar Chhabra ◽  
Dinesh Kumar
Keyword(s):  
Data Clustering ◽  
Euclidean Distance ◽  
Search Algorithm ◽  
Harmony Search ◽  
Real Life ◽  
Optimal Number ◽  
Optimization Strategy ◽  
Number Of Clusters ◽  
Automatic Data ◽  
Parameter Adaptive

AbstractIn this paper, the problem of automatic data clustering is treated as the searching of optimal number of clusters so that the obtained partitions should be optimized. The automatic data clustering technique utilizes a recently developed parameter adaptive harmony search (PAHS) as an underlying optimization strategy. It uses real-coded variable length harmony vector, which is able to detect the number of clusters automatically. The newly developed concepts regarding “threshold setting” and “cutoff” are used to refine the optimization strategy. The assignment of data points to different cluster centers is done based on the newly developed weighted Euclidean distance instead of Euclidean distance. The developed approach is able to detect any type of cluster irrespective of their geometric shape. It is compared with four well-established clustering techniques. It is further applied for automatic segmentation of grayscale and color images, and its performance is compared with other existing techniques. For real-life datasets, statistical analysis is done. The technique shows its effectiveness and the usefulness.

scholarly journals Estimating clique size by coloring the nodes of auxiliary graphs

2018 ◽  
Vol 10 (2) ◽  
pp. 137-157
Author(s):  
Sándor Szabó
Keyword(s):  
Upper Bound ◽  
Clique Number ◽  
Original Graph ◽  
Size Estimate ◽  
Auxiliary Graph

Abstract It is a common practice to find upper bound for clique number via legal coloring of the nodes of the graph. We will point out that with a little extra work we may lower this bound. Applying this procedure to a suitably constructed auxiliary graph one may further improve the clique size estimate of the original graph.

scholarly journals The resolving number of a graph Delia

2013 ◽  
Vol Vol. 15 no. 3 (Graph Theory) ◽  
Author(s):  
Delia Garijo ◽  
Antonio González ◽  
Alberto Márquez
Keyword(s):  
Graph Theory ◽  
Polynomial Time ◽  
Maximum Degree ◽  
Clique Number ◽  
Metric Dimension ◽  
Np Hard ◽  
Arbitrary Graph ◽  
International Audience ◽  
Graph Parameters ◽  
Two Parameters

Graph Theory International audience We study a graph parameter related to resolving sets and metric dimension, namely the resolving number, introduced by Chartrand, Poisson and Zhang. First, we establish an important difference between the two parameters: while computing the metric dimension of an arbitrary graph is known to be NP-hard, we show that the resolving number can be computed in polynomial time. We then relate the resolving number to classical graph parameters: diameter, girth, clique number, order and maximum degree. With these relations in hand, we characterize the graphs with resolving number 3 extending other studies that provide characterizations for smaller resolving number.

scholarly journals Optimal Differential Trails in SIMON-like Ciphers

2017 ◽  
pp. 358-379 ◽  
Author(s):  
Zhengbin Liu ◽  
Yongqiang Li ◽  
Mingsheng Wang
Keyword(s):  
Upper Bound ◽  
Efficient Algorithm ◽  
Search Algorithm ◽  
Hamming Weight ◽  
Differential Probability ◽  
Smt Solvers ◽  
Round Function ◽  
Input Size ◽  
Automatic Search ◽  
First Time

In the present paper, we propose an automatic search algorithm for optimal differential trails in SIMON-like ciphers. First, we give a more accurate upper bound on the differential probability of SIMON-like round function. It is shown that when the Hamming weight of the input difference α , which is denoted by wt(α), is less than one half of the input size, the corresponding maximum differential probability of SIMON-like round function is less than or equal to 2−wt(α)−1. Based on this, we adapt Matsui’s algorithm and propose an efficient algorithm for searching for optimal differential trails. With the proposed algorithm, we find the provably optimal differential trails for 12, 16, 19, 28 and 37 rounds of SIMON32/48/64/96/128. To the best of our knowledge, it is the first time that the provably optimal differential trails for SIMON64, SIMON96 and SIMON128 are reported. The provably optimal differential trails for 13, 19 and 25 rounds of SIMECK32/48/64 are also found respectively, which confirm the results given by Kölbl et al. [KR15]. Besides the optimal differential trails, we also find the 14, 17, 23, 31 and 41-round differentials for SIMON32/48/64/96/128, and 14, 21 and 27-round differentials for SIMECK32/48/64, respectively. As far as we know, these are the best differential distinguishers for SIMON and SIMECK so far. Compared with the approach based on SAT/SMT solvers used by K¨olbl et al., our algorithm is more efficient and more practical to evaluate the security against differential cryptanalysis in the design of SIMON-like ciphers.

scholarly journals Image tampering detection using genetic algorithm

2019 ◽  
Vol 277 ◽  
pp. 02026
Author(s):  
Ritu Agarwal ◽  
Mallika Pant
Keyword(s):  
Genetic Algorithm ◽  
Digital Media ◽  
Digital Images ◽  
Search Algorithm ◽  
Recognition Rate ◽  
Difficult Problem ◽  
Optimal Number ◽  
Support Vector ◽  
Image Forgery ◽  
Selection Algorithms

As digital images become an indispensable source of information, the authentication of digital images has become crucial. Various techniques of forgery have come into existence, intrusive, and non-intrusive. Image forgery detection hence is becoming more challenging by the day, due to the unwavering advances in image processing. Therefore, image forensics is at the forefront of security applications aiming at restoring trust and acceptance in digital media by exposing counterfeiting methods. The proposed work compares between various feature selection algorithms for the detection of image forgery in tampered images. Several features are extracted from normal and spliced images using spatial grey level dependence method and many more. Support vector machine and Twin SVM has been used for classification. A very difficult problem in classification techniques is to pick features to distinguish between classes. Furthermore, The feature optimization problem is addressed using a genetic algorithm (GA) as a search method. At last, classical sequential methods and floating search algorithm are compared against the genetic approach in terms of the best recognition rate achieved and the optimal number of features.

Sign in / Sign up

Export Citation Format

Share Document