Finding the k Smallest Spanning Trees
نویسنده
چکیده
We give improved solutions for the problem of generating the k smallest spanning trees in a graph and in the plane. Our algorithm for general graphs takes time O(m log β(m,n) + k2); for planar graphs this bound can be improved to O(n+ k2). We also show that the k best spanning trees for a set of points in the plane can be computed in time O(min(k2n + n log n, k2 + kn log(n/k))). The k best orthogonal spanning trees in the plane can be found in time O(n log n+ kn log log(n/k) + k2).
منابع مشابه
Ambivalent Data Structures for Dynamic 2-Edge-Connectivity and k Smallest Spanning Trees
Ambivalent data structures are presented for several problems on undirected graphs. They are used in finding the k smallest spanning trees of a weighted undirected graph in Oem log [3(m, n)+min{p/2, km1/ 2 }) time, where m is the number of edges and n the number of vertices in the graph. The techniques can be extended to find the k smallest spanning trees in an embedded planar graph in O(n + k(...
متن کاملk-Best Enumeration
We survey k-best enumeration problems and the algorithms for solving them, including in particular the problems of finding the k shortest paths, k smallest spanning trees, and k best matchings in weighted graphs.
متن کاملAn Algorithm to Generate All Spanning Trees of a Graph in Order of Increasing Cost
A minimum spanning tree of an undirected graph can be easily obtained using classical algorithms by Prim or Kruskal. A number of algorithms have been proposed to enumerate all spanning trees of an undirected graph. Good time and space complexities are the major concerns of these algorithms. Most algorithms generate spanning trees using some fundamental cut or circuit. In the generation process,...
متن کاملK-Smallest Spanning Tree Segmentations
Real-world images often admit many different segmentations that have nearly the same quality according to the underlying energy function. The diversity of these solutions may be a powerful uncertainty indicator. We provide the crucial prerequisite in the context of seeded segmentation with minimum spanning trees (i.e. edge-weighted watersheds). Specifically, we show how to efficiently enumerate...
متن کاملCounting the number of spanning trees of graphs
A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- BIT
دوره 32 شماره
صفحات -
تاریخ انتشار 1990