Spanning Trees in Multipartite Geometric Graphs
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 (Formula presented.). 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 (Formula presented.) 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 (Formula presented.)-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 (Formula presented.) time, where k is the number of different colors (or the size of the multipartition in a complete multipartite geometric graph).
|Keywords||Maximum spanning tree, Minimum spanning tree, Multipartite geometric graphs|
Biniaz, A. (Ahmad), Bose, P, Eppstein, D. (David), Maheshwari, A, Morin, P, & Smid, M. (2017). Spanning Trees in Multipartite Geometric Graphs. Algorithmica, 1–15. doi:10.1007/s00453-017-0375-4