Simple decentralized graph coloring

Galán, Severino F.

doi:10.1007/s10589-016-9862-9

Cited by 18 publications

(8 citation statements)

References 46 publications

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“…Bui et al [17] developed a constructive strategy of coloring scheme based on an ant colony, by which the algorithm produced very consistent results, having very small standard deviations. To color vertexes with given number of color k, Galán [18] developed a decentralized coloring algorithm, where colors of vertexes are modified according to those of the adjacent vertexes. Peng et al [19,20] partitioned a graph G into a set of connected components and a vertex cut component, and combined the separately local colors by an optimized maximum matching based method.…”

Section: Related Workmentioning

confidence: 99%

“…To further improve the quality of obtained color assignment, a local search presented in Algorithm 3 is implemented by the simple decentralized graph coloring (SDGC) algorithm [18] and the tabu search (TS) [38].…”

Section: Local Search In the Solution Spacementioning

confidence: 99%

“…Since a variety of state-of-the-art algorithms are dedicated to address the k-coloring problem [15,17,18,25,27,29,34,35,38], we first try to verify the ability of DEA-PPM to seek a k-coloring scheme, where k is set as the known number of colors for selected benchmark problems. Numerical results are collected for 30 independent runs with 500 generations, and the experimental results are shown in Table 2.…”

Section: Numerical Comparison For the K-coloring Problemmentioning

confidence: 99%

See 2 more Smart Citations

A Distribution Evolutionary Algorithm for Graph Coloring

Xu¹,

Cheng²,

Chen³

et al. 2022

Preprint

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Graph Coloring Problem (GCP) is a classic combinatorial optimization problem that has a wide application in theoretical research and engineering. To address complicated GCPs efficiently, a distribution evolutionary algorithm based on population of probability models (DEA-PPM) is proposed. Based on a novel representation of probability model, DEA-PPM employs a Gaussian orthogonal search strategy to explore the probability space, by which global exploration can be realized using a small population. With assistance of local exploitation on a small solution population, DEA-PPM strikes a good balance between exploration and exploitation. Numerical results demonstrate that DEA-PPM performs well on selected complicated GCPs, which contributes to its competitiveness to the state-of-the-art metaheuristics.

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Section: Related Workmentioning

confidence: 99%

Section: Local Search In the Solution Spacementioning

confidence: 99%

Section: Numerical Comparison For the K-coloring Problemmentioning

confidence: 99%

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A Distribution Evolutionary Algorithm for Graph Coloring

Xu¹,

Cheng²,

Chen³

et al. 2022

Preprint

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“…This method is one of the most basic method of graph colouring. It assigns the smallest possible colour to vertices such that no conflict exists between the vertices and their coloured neighbours (Galán, 2017). The process is shown in Algorithm 1.…”

Section: Greedy Algorithmmentioning

confidence: 99%

Minimizing Interference in Ultra-Dense Femtocell Networks Using Graph-Based Frequency Reuse Technique

Adekunle¹,

Gbenga-Ilori

2020

FUOYEJET

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This paper investigates the performance of graph colouring schemes for frequency assignment in Long-Term Evolution (LTE) networks with ultra-dense femtocells. The aim of the study is to minimize interference in such networks while ensuring efficient spectrum use for these femtocells. The three schemes investigated are the conventional greedy graph colouring algorithm, the saturation degree algorithm and our proposed graph-based theory (GBT) algorithm. The process of frequency assignment is similar in the last two except that the proposed GBT partitions the femtocells into independent sets for an efficient frequency re-use. The performance of these three schemes was analyzed through extensive simulations to determine the SINR and network capacity that can be obtained with the deployment of these schemes using the ITU-R P1238-7 path loss model. The outcome of this study showed that with the absence of a dynamic frequency assignment scheme, interference level is increased as the number of femtocell users within a particular coverage is increased, leading to a reduction in the capacity of such networks. Simulation results showed that all three algorithms considered have the ability to allocate frequencies to femtocells and minimize interference in a densely deployed environment, thereby increasing network capacity. The proposed GBT assigned the least sub-band thereby ensuring spectral efficiency while minimizing harmful interference. Results show that the greedy algorithm has a disadvantage of inefficiently assigning sub-bands randomly, while the saturation degree assigns more sub-bands when compared with the GBT scheme.Keywords — Femtocell, graph colouring, frequency assignment, LTE.

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“…Tabu search [17], backtracking [18], branch and bound [11], evolutionary algorithm [19][20][21], branch and cut [22], particle swarm optimization (PSO) [23][24][25][26], ant colony optimization (ACO) [27], local and cuckoo search [28,29] are some existing methods for finding χ(G). Some recent applications of GCP are selective graph coloring [30,31], signed graphs coloring [32,33], scheduling, and resource allocation [7][8][9][10][34][35][36][37][38]. In comparison to other methods, GA is useful for solving multi-objective optimization problems with vast search space.…”

Section: Introductionmentioning

confidence: 99%

Complexity Analysis and Stochastic Convergence of Some Well-known Evolutionary Operators for Solving Graph Coloring Problem

Marappan

Sethumadhavan

2020

Mathematics

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The graph coloring problem is an NP-hard combinatorial optimization problem and can be applied to various engineering applications. The chromatic number of a graph G is defined as the minimum number of colors required to color the vertex set V(G) so that no two adjacent vertices are of the same color, and different approximations and evolutionary methods can find it. The present paper focused on the asymptotic analysis of some well-known and recent evolutionary operators for finding the chromatic number. The asymptotic analysis of different crossover and mutation operators helps in choosing the better evolutionary operator to minimize the problem search space and computational complexity. The choice of the right genetic operators facilitates an evolutionary algorithm to achieve faster convergence with lesser population size N through an adequate distribution of promising genes. The selection of an evolutionary operator plays an essential role in reducing the bounds for minimum color obtained so far for some of the benchmark graphs. This research also focuses on the necessary and sufficient conditions for the global convergence of evolutionary algorithms. The stochastic convergence of recent evolutionary operators for solving graph coloring is newly analyzed.

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Simple decentralized graph coloring

Cited by 18 publications

References 46 publications

A Distribution Evolutionary Algorithm for Graph Coloring

A Distribution Evolutionary Algorithm for Graph Coloring

Minimizing Interference in Ultra-Dense Femtocell Networks Using Graph-Based Frequency Reuse Technique

Complexity Analysis and Stochastic Convergence of Some Well-known Evolutionary Operators for Solving Graph Coloring Problem

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