Kab Kevin Verbeek

Area-Universal and Constrained Rectangular Layouts

A rectangular layout is a partition of a rectangle into a finite set of interior-disjoint rectangles. These layouts are used as rectangular cartograms in cartography, as floorplans in building architecture and VLSI design, and as graph drawings. Often areas are associated with the rectangles of a rectangular layout and it is desirable for one rectangular layout to represent several area assignments. A layout is area-universal if any assignment of areas to rectangles can be realized by a combinatorially equivalent rectangular layout. We identify a simple necessary and sufficient condition for a rectangular layout to be area-universal: a rectangular layout is area-universal if and only if it is one-sided. We also investigate similar questions for perimeter assignments. The adjacency requirements for the rectangles of a rectangular layout can be specified in various ways, most commonly via the dual graph of the layout. We show how to find an area-universal layout for a given set of adjacency requirements whe...

Area-universal rectangular layouts

A rectangular layout is a partition of a rectangle into a finite set of interior-disjoint rectangles. They are used as rectangular cartograms in cartography, as floorplans in building architecture and VLSI design, and as graph drawings. Often areas are associated with the rectangles of a rectangular layout and it is desirable for one rectangular layout to represent several area assignments. A layout is area-universal if any assignment of areas to rectangles can be realized by a combinatorially equivalent rectangular layout. We identify a simple necessary and sufficient condition for a rectangular layout to be area-universal: a rectangular layout is area-universal if and only if it is one-sided. We also investigate similar questions for perimeter assignments. The adjacency requirements for the rectangles of a rectangular layout can be specified in various ways, most commonly via the dual graph of the layout. We show how to find an area-universal layout for a given set of adjacency requirements whenever such a layout exists.

Homotopic C -oriented routing

We study the problem of finding non-crossing minimum-link

Metric embedding, hyperbolic space, and social networks

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Bundled Crossings in Embedded Graphs

-oriented paths that are homotopic to a set of input paths in an environment with

Stable Treemaps via Local Moves

\mathcal{C}

Homotopic C-oriented routing with few links and thick edges

-oriented obstacles. We introduce a special type of

Complexity Measures for Mosaic Drawings

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Computing representative networks for braided rivers

-oriented paths--smooth paths--and present a 2-approximation algorithm that runs in O(n2 (n+logκ)+kin logn) time, where n is the total number of paths and obstacle vertices, kin is the total number of links in the input, and κ = |

Non-crossing Paths with Geographic Constraints

\mathcal{C}