Effective and efficient dynamic graph coloring

Abstract

Graph coloring is a fundamental graph problem that is widely applied in a variety of applications. The aim of graph coloring is to minimize the number of colors used to color the vertices in a graph such that no two incident vertices have the same color. Existing solutions for graph coloring mainly focus on computing a good coloring for a static graph. However, since many real-world graphs are highly dynamic, in this paper, we aim to incrementally maintain the graph coloring when the graph is dynamically updated. We target on two goals: high effectiveness and high efficiency. To achieve high effectiveness, we maintain the graph coloring in a way such that the coloring result is consistent with one of the best static graph coloring algorithms for large graphs. To achieve high efficiency, we investigate efficient incremental algorithms to update the graph coloring by exploring a small number of vertices. We design a color-propagation based algorithm which only explores the vertices within the 2-hop neighbors of the update-related and color-changed vertices. We then propose a novel color index to maintain some summary color information and, thus, bound the explored vertices within the neighbors of these vertices. Moreover, we derive some effective pruning rules to further reduce the number of propagated vertices. The experimental results demonstrate the high effectiveness and efficiency of our approach. PVLDB Reference Format:

UAV-Assisted Emergency Communications in Social IoT: A Dynamic Hypergraph Coloring Approach

“…Coloring consistency can save the channel switch cost by avoiding unnecessary channel allocation triggered by the dynamics [25]. In [26], the authors proposed a colorpropagation based algorithm by exploring a small part of vertexes in each update, and thus the complexity is further reduced. In [27], the authors introduced the dynamic graph coloring into D2D communications.…”

“…For the dynamic spectrum sharing problem, we depict this problem with the framework of hypergraph and simplify the hypergraph structure to a directed graph. Based on the technique for dynamic graph coloring in [26], we propose a dynamic hypergraph coloring approach to maintain the mutual interference level with the lower channel switching cost guaranteed, when the graph is dynamically updated. • Validations: We comprehensively prove the global stability, convergence, and complexity properties of our proposed approach.…”

“…Last but not least, under various scenarios, simulation results demonstrate that our proposed approach can achieve a better trade-off between the information diffusion speed and complexity compared with existing methods. Note that the main idea of the technique for dynamic graph coloring comes from [26], but there are some differences between [26] and our work. Firstly, the authors in [26] solved the dynamic coloring problem in conventional graph, in which one edge can only connect two nodes.…”

“…Note that the main idea of the technique for dynamic graph coloring comes from [26], but there are some differences between [26] and our work. Firstly, the authors in [26] solved the dynamic coloring problem in conventional graph, in which one edge can only connect two nodes. Considering that the conventional graph cannot accurately model the cumulative mutual interferences from more than one interference source, we conceive the dynamic network topology with hypergraph, in which one edge can connect more than two nodes.…”

A Hybrid Exam Scheduling Technique based on Graph Coloring and Genetic Algorithms Targeted towards Student Comfort

“…They take into consideration random and heuristic changes on the graph. Graph coloring for dynamic graphs is also investigated in [8] where authors focus on a technique to ensure high effectiveness and high efficiency. They achieve that by performing incremental color propagation as the graph changes.…”