scholarly journals Constructive algorithms for the partial directed weighted improper coloring problem

2016 ◽  
Vol 20 (2) ◽  
pp. 159-188 ◽  
Author(s):  
Alain Hertz ◽  
Romain Montagné ◽  
François Gagnon
Keyword(s):  
Constructive Algorithms ◽  
Coloring Problem ◽  
Improper Coloring

scholarly journals IMPROPER COLORING OF WEIGHTED GRID AND HEXAGONAL GRAPHS

2010 ◽  
Vol 02 (03) ◽  
pp. 395-411 ◽  
Author(s):  
JEAN-CLAUDE BERMOND ◽  
FRÉDÉRIC HAVET ◽  
FLORIAN HUC ◽  
CLÁUDIA LINHARES SALES
Keyword(s):  
Approximation Algorithms ◽  
Triangular Lattice ◽  
Allocation Problem ◽  
Approximation Ratio ◽  
Exact Results ◽  
Proper Coloring ◽  
Frequency Allocation ◽  
Coloring Problem ◽  
Improper Coloring ◽  
General Graphs

We study a weighted improper coloring problem motivated by a frequency allocation problem. It consists of associating to each vertex a set of p(v) (weight) distinct colors (frequencies), such that the set of vertices having a given color induces a graph of degree at most k (the case k = 0 corresponds to proper coloring). The objective is to minimize the number of colors. We propose approximation algorithms to compute such a coloring for general graphs. We apply these to obtain good approximation ratio for grid and hexagonal graphs. Furthermore we give exact results for the 2-dimensional grid and the triangular lattice when the weights are all the same.

A DNA computer model for solving vertex coloring problem

2006 ◽  
Vol 51 (20) ◽  
pp. 2541-2549 ◽  
Author(s):  
Jin Xu ◽  
Xiaoli Qiang ◽  
Fang Gang ◽  
Kang Zhou
Keyword(s):  
Computer Model ◽  
Vertex Coloring ◽  
Coloring Problem ◽  
Vertex Coloring Problem ◽  
Dna Computer

A parallel biological computing algorithm to solve the vertex coloring problem with polynomial time complexity

2021 ◽  
pp. 1-11
Author(s):  
Zhaocai Wang ◽  
Dangwei Wang ◽  
Xiaoguang Bao ◽  
Tunhua Wu
Keyword(s):  
Time Complexity ◽  
Optimization Problems ◽  
Combinatorial Problem ◽  
Vertex Coloring ◽  
Intelligent Computing ◽  
Coloring Problem ◽  
Combinatorial Optimization Problems ◽  
Computing Algorithm ◽  
Vertex Coloring Problem ◽  
Dna Algorithm

The vertex coloring problem is a well-known combinatorial problem that requires each vertex to be assigned a corresponding color so that the colors on adjacent vertices are different, and the total number of colors used is minimized. It is a famous NP-hard problem in graph theory. As of now, there is no effective algorithm to solve it. As a kind of intelligent computing algorithm, DNA computing has the advantages of high parallelism and high storage density, so it is widely used in solving classical combinatorial optimization problems. In this paper, we propose a new DNA algorithm that uses DNA molecular operations to solve the vertex coloring problem. For a simple n-vertex graph and k different kinds of color, we appropriately use DNA strands to indicate edges and vertices. Through basic biochemical reaction operations, the solution to the problem is obtained in the O (kn2) time complexity. Our proposed DNA algorithm is a new attempt and application for solving Nondeterministic Polynomial (NP) problem, and it provides clear evidence for the ability of DNA calculations to perform such difficult computational problems in the future.

scholarly journals On the max-weight edge coloring problem

2009 ◽  
Vol 20 (4) ◽  
pp. 429-442 ◽  
Author(s):  
Giorgio Lucarelli ◽  
Ioannis Milis ◽  
Vangelis T. Paschos
Keyword(s):  
Edge Coloring ◽  
Coloring Problem

A CONSTRUCTIVE ALGORITHM THAT CONVERGES FOR REAL-VALUED INPUT PATTERNS

1994 ◽  
Vol 05 (01) ◽  
pp. 59-66 ◽  
Author(s):  
NEIL BURGESS
Keyword(s):  
Constructive Algorithms ◽  
Constructive Algorithm ◽  
Cascade Correlation ◽  
Specific Error

A constructive algorithm is presented which combines the architecture of Cascade Correlation and the training of perceptron-like hidden units with the specific error-correcting roles of Upstart. Convergence to zero errors is proved for any consistent classification of real-valued pattern vectors. Addition of one extra element to each pattern allows hyper-spherical decision regions and enables convergence on real-valued inputs for existing constructive algorithms. Simulations demonstrate robust convergence and economical construction of hidden units in the benchmark “N-bit parity” and “twin spirals” problems.

Tabu Assisted Local Search for the Minimum Load Coloring Problem

2014 ◽  
Vol 11 (12) ◽  
pp. 2476-2480 ◽  
Author(s):  
Ansheng Ye ◽  
Zhiqiang Zhang ◽  
Xiaoqing Zhou ◽  
Fang Miao
Keyword(s):  
Local Search ◽  
Coloring Problem
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