Non-crossing matchings of points with geometric objects
Given an ordered set of points and an ordered set of geometric objects in the plane, we are interested in finding a non-crossing matching between point–object pairs. In this paper, we address the algorithmic problem of determining whether a non-crossing matching exists between a given point–object p...
| Main Authors: | , , , , , , , , , , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Elsevier
2015
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| Online Access: | http://hdl.handle.net/1721.1/99978 https://orcid.org/0000-0003-3803-5703 |
| Summary: | Given an ordered set of points and an ordered set of geometric objects in the plane, we are interested in finding a non-crossing matching between point–object pairs. In this paper, we address the algorithmic problem of determining whether a non-crossing matching exists between a given point–object pair. We show that when the objects we match the points to are finite point sets, the problem is NP-complete in general, and polynomial when the objects are on a line or when their size is at most 2. When the objects are line segments, we show that the problem is NP-complete in general, and polynomial when the segments form a convex polygon or are all on a line. Finally, for objects that are straight lines, we show that the problem of finding a min-max non-crossing matching is NP-complete. |
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