Research output per year
Research output per year
Steven Chaplick, Stefan Felsner, Philipp Kindermann, Jonathan Klawitter*, Ignaz Rutter, Alexander Wolff
Research output: Contribution to journal › Article › Academic › peer-review
A rectangular dual of a graph G is a contact representation of G by axis-aligned rectangles such that (i) no four rectangles share a point and (ii) the union of all rectangles is a rectangle. The partial representation extension problem for rectangular duals asks whether a given partial rectangular dual can be extended to a rectangular dual, that is, whether there exists a rectangular dual where some vertices are represented by prescribed rectangles. The simultaneous representation problem for rectangular duals asks whether two (or more) given graphs that share a subgraph admit rectangular duals that coincide on the shared subgraph. Combinatorially, a rectangular dual can be described by a regular edge labeling (REL), which determines the orientations of the rectangle contacts. We describe linear-time algorithms for the partial representation extension problem and the simultaneous representation problem for rectangular duals when each input graph is given together with a REL. Both algorithms are based on formulations as linear programs, yet they have geometric interpretations and can be seen as extensions of the classic algorithm by Kant and He that computes a rectangular dual for a given graph.
Original language | English |
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Pages (from-to) | 66-74 |
Number of pages | 9 |
Journal | Theoretical Computer Science |
Volume | 919 |
DOIs | |
Publication status | Published - 5 Jun 2022 |
Research output: Working paper / Preprint › Preprint
Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic