2016/11/05 by Ahmad Biniaz, Prosenjit Bose, Biniaz, Ahmad +9
Computer Science · Engineering · #3D Modeling in Geospatial Applications #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #Data Management and Algorithms #FOS: Computer and information sciences #cs.CG
paper · pdf · doi:10.48550/arxiv.1611.01661
13 pages
arxiv created 2016/11/05 · openalex publication_date 2016/11/05 · arxiv updated 2016/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R and B be two disjoint sets of points in the plane where the points of R are colored red and the points of B are colored blue, and let n=|R∪ B|. A bichromatic spanning tree is a spanning tree in the complete bipartite geometric graph with bipartition (R,B). The minimum (respectively maximum) bichromatic spanning tree problem is the problem of computing a bichromatic spanning tree of minimum (respectively maximum) total edge length. 1. We present a simple algorithm that solves the minimum bichromatic spanning tree problem in O(nlog3 n) time. This algorithm can easily be extended to solve the maximum bichromatic spanning tree problem within the same time bound. It also can easily be generalized to multicolored point sets. 2. We present Θ(nlog n)-time algorithms that solve the minimum and the maximum bichromatic spanning tree problems. 3. We extend the bichromatic spanning tree algorithms and solve the multicolored version of these problems in O(nlog nlog k) time, where k is the number of different colors (or the size of the multipartition in a complete multipartite geometric graph).