Non-crossing Connectors in the Plane

Details Non-crossing Connectors in the Plane Non-crossing Connectors in the Plane

2012-01-04

arxiv.org/abs/1201.0917v1

Computer Science

Computational Geometry

Scientific paper

We consider the non-crossing connectors problem, which is stated as follows: Given n simply connected regions R_1,...,R_n in the plane and finite point sets P_i subset of R_i for i=1,...,n, are there non-crossing connectors y_i for (R_i,P_i), i.e., arc-connected sets y_i with P_i subset of y_i subset of R_i for every i=1,...,n, such that y_i and y_j are disjoint for all i different from j? We prove that non-crossing connectors do always exist if the regions form a collection of pseudo-disks, i.e., the boundaries of every pair of regions intersect at most twice. We provide a simple polynomial-time algorithm if the regions are axis-aligned rectangles. Finally we prove that the general problem is NP-complete, even if the regions are convex, the boundaries of every pair of regions intersect at most four times and P_i consists of only two points on the boundary of R_i for i=1,...,n.

Affiliated with

Also associated with

No associations

Rating

Non-crossing Connectors in the Plane does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Non-crossing Connectors in the Plane, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Non-crossing Connectors in the Plane will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-156739