The maximum k-differential coloring problem

Bekos, Michael A.; Kaufmann, Michael; Kobourov, Stephen G.; Stavropoulos, Konstantinos S.; Veeramoni, Sankar

doi:10.1016/j.jda.2017.08.001

Cited by 2 publications

(1 citation statement)

References 27 publications

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“…We try to assign perceptually different colors to lines with the help of a greedy heuristic to optimize color difference between adjacent lines. Note that the underlying problem, known as max differential coloring, is NP-hard [10].…”

Section: Map Rendering and Interface 41 Metro Map Renderingmentioning

confidence: 99%

MetroSets: Visualizing Sets as Metro Maps

Jacobsen

Wallinger

Kobourov

et al. 2021

IEEE Trans. Visual. Comput. Graphics

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We propose MetroSets, a new, flexible online tool for visualizing set systems using the metro map metaphor. We model a given set system as a hypergraph H = (V, S), consisting of a set V of vertices and a set S, which contains subsets of V called hyperedges. Our system then computes a metro map representation of H, where each hyperedge E in S corresponds to a metro line and each vertex corresponds to a metro station. Vertices that appear in two or more hyperedges are drawn as interchanges in the metro map, connecting the different sets. MetroSets is based on a modular 4-step pipeline which constructs and optimizes a path-based hypergraph support, which is then drawn and schematized using metro map layout algorithms. We propose and implement multiple algorithms for each step of the MetroSet pipeline and provide a functional prototype with easy-to-use preset configurations. Furthermore, using several real-world datasets, we perform an extensive quantitative evaluation of the impact of different pipeline stages on desirable properties of the generated maps, such as octolinearity, monotonicity, and edge uniformity.

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Section: Map Rendering and Interface 41 Metro Map Renderingmentioning

confidence: 99%

MetroSets: Visualizing Sets as Metro Maps

Jacobsen

Wallinger

Kobourov

et al. 2021

IEEE Trans. Visual. Comput. Graphics

View full text Add to dashboard Cite

show abstract

Contrast in greyscales of graphs

et al. 2020

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In this work we present the notion of greyscale of a graph as a colouring of its vertices that uses colours from the real interval [0,1]. Any greyscale induces another colouring by assigning to each edge the non-negative difference between the colours of its vertices. These edge colours are ordered in lexicographical increasing ordering and gives rise to a new element of the graph: the contrast vector. We introduce the notion of maximum contrast vector (in the set of contrast vectors of all possible greyscales defined on the graph) as a new invariant for the graph. The relation between finding the maximum contrast vector for the graph and its chromatic number is established. Thus the maximum contrast problem is an NP-complete problem. However, the set of values of any maximum contrast greyscale for any graph is bounded by a finite set which is given. Several methods to compute the maximum contrast vector with some restrictions are collected in this paper.The interest of these new concepts lies in their possible applications for solving problems of engineering, physics and applied mathematics which are modeled according to a network whose nodes have assigned numerical values of a certain parameter delimited by a range of real numbers. The objective is to maximize the differences between each node and its neighbors, from a local and global point of view simultaneously through a vectorial objective function, that is the contrast vector.

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The maximum k-differential coloring problem

Cited by 2 publications

References 27 publications

MetroSets: Visualizing Sets as Metro Maps

MetroSets: Visualizing Sets as Metro Maps

Contrast in greyscales of graphs

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