Complexity of Fall Coloring for Restricted Graph Classes

Lauri, Juho; Mitillos, Christodoulos

doi:10.1007/978-3-030-25005-8_29

Cited by 3 publications

(2 citation statements)

References 19 publications

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“…Li et al [11] proposed the relaxation model, and the time complexity of the simulated annealing algorithm is analyzed by the dynamic setting of the Markov chain length and the dynamical system model. Tools and methods for computational time complexity analysis of EAs are constantly emerging [14][15][16][17][18]. However, the comparative analysis of EAs is not an easy job.…”

Section: Introductionmentioning

confidence: 99%

Comparative Analysis of (1 + λ)Evolutionary Algorithms Based on Comparison-in-time Model

Feng

Zhou

Tan

et al. 2022

Preprint

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Runtime comparative analysis of evolutionary algorithms (EAs) is an important topic in the theoretical research of evolutionary computation. Few studies have been conducted to compare the performance of the runtime analysis. The runtime of EAs can be measured by the first hitting time (FHT) to find the optimal solution. In this paper, we present the design of an equal-in-time model based on the stochastic process model of FHT and the property of equivalence relation, which realizes by expected FHT (EFHT) equivalence class division of difference EAs. With the equal-in-time model, we propose a comparison-in-time model, which can directly compare and analyze the EFHT of different EAs. To verify the feasibility of the proposed comparison-in-time model on a multi-individual population, we conducted a case study to analyze the performance of (1 + λ)EA with different selection operators and different variation operators. Experimental results show that the proposed comparison-in-time model is applicable to the comparison of (1 + λ)EA and is consistent with the comparative analysis results of (1 + 1)EA.

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Section: Introductionmentioning

confidence: 99%

Comparative Analysis of (1 + λ)Evolutionary Algorithms Based on Comparison-in-time Model

Feng

Zhou

Tan

et al. 2022

Preprint

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“…However, since the corresponding Fall Coloring problem falls in the category of locally checkable vertex partitioning problems, it has been shown in earlier work of Telle and Proskurowski [40] to be FPT parameterized by the number of colors plus the treewidth of the input graph, and by Heggernes and Telle [21] to be NP-complete for fixed number of colors. Fall Coloring remains hard further restricted to bipartite [28,29,38], chordal [38], or planar [29] graphs. On the other hand, even with unbounded number of colors, it is known to be solvable in polynomial time on strongly chordal graphs [31,17], threshold graphs and split graphs [33].…”

Section: Introductionmentioning

confidence: 99%

b-Coloring Parameterized by Clique-Width

Jaffke¹,

Lima²,

Lokshtanov³

2020

Preprint

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We provide a polynomial-time algorithm for b-Coloring on graphs of constant clique-width. This unifies and extends previously known polynomial-time results on several graph classes, and answers open questions posed by Campos and Silva [Algorithmica, 2018] and Bonomo et al. [Graphs Combin., 2009]. This constitutes the first result concerning structural parameterizations of this problem. We show that the problem is FPT when parameterized by the vertex cover number on general graphs, and on chordal graphs when parameterized by the number of colors. Additionally, we observe that our algorithm for graphs of bounded clique-width can be adapted to solve the Fall Coloring problem within the same runtime bound.

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b-Coloring Parameterized by Clique-Width

Jaffke,

Lima,

Lokshtanov

2023

Theory Comput Syst

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We provide a polynomial-time algorithm for b-Coloring on graphs of constant clique-width. This unifies and extends nearly all previously known polynomial time results on graph classes, and answers open questions posed by Campos and Silva (Algorithmica 80(1), 104–115, 2018) and Bonomo et al. (Graphs and Combinatorics 25(2), 153–167, 2009). This constitutes the first result concerning structural parameterizations of this problem. We show that the problem is $$\textsf{FPT}$$ FPT when parameterized by the vertex cover number on general graphs, and on chordal graphs when parameterized by the number of colors. Additionally, we observe that our algorithm for graphs of bounded clique-width can be adapted to solve the Fall Coloring problem within the same runtime bound. The running times of the clique-width based algorithms for $$b$$ b -Coloring and Fall Coloring are tight under the Exponential Time Hypothesis.

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Complexity of Fall Coloring for Restricted Graph Classes

Cited by 3 publications

References 19 publications

Comparative Analysis of (1 + λ)Evolutionary Algorithms Based on Comparison-in-time Model

Comparative Analysis of (1 + λ)Evolutionary Algorithms Based on Comparison-in-time Model

b-Coloring Parameterized by Clique-Width

b-Coloring Parameterized by Clique-Width

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