Record link: 
http://hdl.handle.net/20.500.12708/203884
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Title: 
Minimizing Corners in Colored Rectilinear Grids
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Citation: 
Depian, T., Dobler, A., Wulms, J., & Kern, C. (2024). Minimizing Corners in Colored Rectilinear Grids. In WALCOM: Algorithms and Computation - 18th International Conference and Workshops on Algorithms and Computation, WALCOM 2024, Kanazawa, Japan, March 18–20, 2024, Proceedings (pp. 134–148). Springer, Singapore.
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Publication Type: 
Inproceedings - Full-Paper Contribution
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Language: 
English
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Authors: 
Depian, Thomas 
Dobler, Alexander 
Wulms, Jules 
Kern, Christoph 
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Organisational Unit: 
E192 - Institut für Logic and Computation 
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Published in: 
WALCOM: Algorithms and Computation - 18th International Conference and Workshops on Algorithms and Computation, WALCOM 2024, Kanazawa, Japan, March 18–20, 2024, Proceedings 
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Volume: 
14549
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Date (published): 
29-Feb-2024
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Event name: 
18th International Conference and Workshops on Algorithms and Computation, WALCOM 2024) 
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Event date: 
18-Mar-2024 - 20-Mar-2024
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Event place: 
Kanazawa, Japan
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Number of Pages: 
15
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Publisher: 
Springer, Singapore
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Peer reviewed: 
Yes
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Keywords: 
shape complexity; rectilinear polygons; set visualization
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Abstract: 
Given a rectilinear grid G, in which cells are either assigned a single color, out of k possible colors, or remain white, can we color white grid cells of G to minimize the total number of corners of the resulting colored rectilinear polygons in G? We show how this problem relates to hypergraph visualization, prove that it is NP-hard even for k = 2, and present an exact dynamic programming algorithm. Together with a set of simple kernelization rules, this leads to an FPT-algorithm in the number of colored cells of the input. We additionally provide an XP-algorithm in the solution size, and a polynomial O (OP T)-approximation algorithm.
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Research Areas: 
Logic and Computation: 100%
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Science Branch: 
1020 - Informatik: 80%
1010 - Mathematik: 20%
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