Covering oriented points in the plane with orthogonal polygons is NP-complete

Evrendilek, Cem; Genç, Burkay; Hnich, Brahim

doi:10.1016/j.endm.2010.05.039

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Cited by 4 publications

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“…For simplicity, we use the term monotonicity to refer to x-monotonicity.2 After this paper was accepted for publication, the authors learned of a similar result obtained independently by Evrendilek et al that appeared in the Proceedings of the 2010 International Symposium on Combinatorial Optimization[11]. The hardness results of Section 2 were first presented by Biedl et al in a workshop abstract[4] and conference proceedings[5].…”

mentioning

confidence: 90%

Reconstructing polygons from scanner data

Biedl

Durocher

Snoeyink

2011

Theoretical Computer Science

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mentioning

confidence: 90%

Reconstructing polygons from scanner data

Biedl

Durocher

Snoeyink

2011

Theoretical Computer Science

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Reconstructing Polygons from Scanner Data

Biedl

Durocher²,

Snoeyink

2009

Algorithms and Computation

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A range-finding scanner can collect information about the shape of an (unknown) polygonal room in which it is placed. Suppose that a set of scanners returns not only a set of points, but also additional information, such as the normal to the plane when a scan beam detects a wall. We consider the problem of reconstructing the floor plan of a room from different types of scan data. In particular, we present algorithmic and hardness results for reconstructing two-dimensional polygons from point-wall pairs, point-normal pairs, and visibility polygons. The polygons may have restrictions on topology (e.g., to be simply connected) or geometry (e.g., to be orthogonal). We show that this reconstruction problem is NP-hard under most models, but that some restrictive assumptions do allow polynomialtime reconstruction algorithms.

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