Faster bottleneck non-crossing matchings of points in convex position

Savić, Marko; Stojaković, Miloš

doi:10.1016/j.comgeo.2017.05.002

Cited by 4 publications

(2 citation statements)

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“…This was accompanied by an O(n 3 )-time algorithm when the points are in convex position. Recently this was improved to O(n 2 ) time by Savić and Stojaković [12]. For bichromatic point sets, Carlsson et al [6] showed that finding a MinMax matching is also N Phard.…”

Section: Previous Work On Perfect Non-crossing Matchingsmentioning

confidence: 99%

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New variants of Perfect Non-crossing Matchings

Mantas,

Savić,

Schrezenmaier

2020

Preprint

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Given a set of points in the plane, we are interested in matching them with straight line segments. We focus on perfect (all points are matched) non-crossing (no two edges intersect) matchings. Apart from the well known MinMax variation, where the length of the longest edge is minimized, we extend work by looking into different optimization variants such as MaxMin, MinMin and MaxMax. We consider both the monochromatic and bichromatic versions of these problems and provide efficient algorithms for various input point configurations.

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Section: Previous Work On Perfect Non-crossing Matchingsmentioning

confidence: 99%

“…Remarks in this section. We believe that o(n 3 )-time algorithms can be devised for MaxMin by using some ideas similar to those used for MinMax in [12,13].…”

Section: Minmin2 and Maxmax2 Matchings In Convex Positionmentioning

confidence: 99%