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STACS
2010
Springer

Long Non-crossing Configurations in the Plane

11 years 6 months ago
Long Non-crossing Configurations in the Plane
We revisit several maximization problems for geometric networks design under the non-crossing constraint, first studied by Alon, Rajagopalan and Suri (ACM Symposium on Computational Geometry, 1993). Given a set of n points in the plane in general position (no three points collinear), compute a longest non-crossing configuration composed of straight line segments that is: (a) a matching (b) a Hamiltonian path (c) a spanning tree. Here we obtain new results for (b) and (c), as well as for the Hamiltonian cycle problem: (i) For the longest non-crossing Hamiltonian path problem, we give an approximation algorithm with ratio 2 π+1 ≈ 0.4829. The previous best ratio, due to Alon et al., was 1/π ≈ 0.3183. Moreover, the ratio of our algorithm is close to 2/π on a relatively broad class of instances: for point sets whose perimeter (or diameter) is much shorter than the maximum length matching. The algorithm runs in O(n7/3 log n) time. (ii) For the longest non-crossing spanning tree prob...
Noga Alon, Sridhar Rajagopalan, Subhash Suri
Added 14 May 2010
Updated 14 May 2010
Type Conference
Year 2010
Where STACS
Authors Noga Alon, Sridhar Rajagopalan, Subhash Suri
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