منابع مشابه
Compatible Matchings for Bichromatic Plane Straight-line Graphs
Two plane graphs with the same vertex set are compatible if their union is again a plane graph. We consider bichromatic plane straight-line graphs with vertex set S consisting of the same number of red and blue points, and (perfect) matchings which are compatible to them. For several different classes C of graphs, we present lower and upper bounds such that any given graph G(S) ∈ C admits a com...
متن کاملBottleneck Bichromatic Non-crossing Matchings using Orbits
Let R and B be sets of n red and n blue points in the plane, respectively, with P = R∪ B. Let M be a perfect matching between points from R and B, using n straight line segments to match the points, that is, each point is an endpoint of exactly one line segment, and each line segment has one red and one blue endpoint. We forbid line segments to cross. Denote the length of a longest line segment...
متن کاملCompatible geometric matchings
This paper studies non-crossing geometric perfect matchings. Two such perfect matchings are compatible if they have the same vertex set and their union is also non-crossing. Our first result states that for any two perfect matchings M and M ′ of the same set of n points, for some k ∈ O(log n), there is a sequence of perfect matchings M = M0,M1, . . . ,Mk = M , such that each Mi is compatible wi...
متن کاملQuasi - Parallel Segments and Characterization of 1 Unique Bichromatic Matchings
5 Given n red and n blue points in general position in the plane, it is well-known 6 that there is a perfect matching formed by non-crossing line segments. We charac-7 terize the bichromatic point sets which admit exactly one non-crossing matching. 8 We give several geometric descriptions of such sets, and find an O(n log n) algorithm 9 that checks whether a given bichromatic set has this prope...
متن کاملQuasi-parallel Segments and Characterizations of Unique Bichromatic Matchings
Given a set of n blue and n red points in general position in the plane, it is well-known that there is at least one bichromatic perfect matching realized by non-crossing straight line segments. We characterize the situation in which such a point set has exactly one matching M of this kind. In this case, we say that M is a unique matching. We find several geometric descriptions of unique matchi...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2015
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2014.08.009