Grid-Obstacle Representations with Connections to Staircase Guarding

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10692)


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.


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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada

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