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- W2743128558 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 textsc{NP}-hard in 2D." @default.
- W2743128558 created "2017-08-17" @default.
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- W2743128558 date "2017-08-06" @default.
- W2743128558 modified "2023-09-27" @default.
- W2743128558 title "Grid-Obstacle Representations with Connections to Staircase Guarding" @default.
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