Quasi-Parallel Segments and Characterization of Unique Bichromatic Matchings
نویسندگان
چکیده
Given n red and n blue points in general position in the plane, it is well-known that there is a perfect matching formed by non-crossing line segments. We characterize the bichromatic point sets which admit exactly one non-crossing matching. We give several geometric descriptions of such sets, and find an O(n log n) algorithm that checks whether a given bichromatic set has this property.
منابع مشابه
Quasi - 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...
متن کاملPerfect Bipartite Matching in Pseudo-Deterministic RNC
In this paper we present a pseudo-deterministic RNC algorithm for finding perfect matchings in bipartite graphs. Specifically, our algorithm is a randomized parallel algorithm which uses poly(n) processors, poly(log n) depth, poly(log n) random bits, and outputs for each bipartite input graph a unique perfect matching with high probability. That is, it returns the same matching for almost all r...
متن کاملCompatible 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- JoCG
دوره 6 شماره
صفحات -
تاریخ انتشار 2015