Grid-Obstacle Representations with Connections to Staircase Guarding

Biedl, Therese and Mehrabi, Saeed Grid-Obstacle Representations with Connections to Staircase Guarding. In: Graph Drawing and Network Visualization, GD 2017, September 25-27 , pp. 81-87(Official URL: https://doi.org/10.1007/978-3-319-73915-1_7).

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Abstract

In this paper, we study grid-obstacle representations of graphs where we assign grid-points to vertices and define obstacles such that an edge exists if and only if an xy-monotone grid path connects the two endpoints without hitting an obstacle or another vertex. It was previously argued that all planar graphs have a grid-obstacle representation in 2D, and all graphs have a grid-obstacle representation in 3D. In this paper, we show that such constructions are possible with significantly smaller grid-size than previously achieved. Then we study the variant where vertices are not blocking, and show that then grid-obstacle representations exist for bipartite graphs. The latter has applications in so-called staircase guarding of orthogonal polygons; using our grid-obstacle representations, we show that staircase guarding is NP-hard in 2D.

Item Type: Conference Paper
Classifications: P Styles > P.900 Visibility
P Styles > P.999 Others
URI: http://gdea.informatik.uni-koeln.de/id/eprint/1592

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