Counting Minimum Weight Spanning Trees
نویسندگان
چکیده
We present an algorithm for counting the number of minimum weight spanning trees, based on the fact that the generating function for the number of spanning trees of a given graph, by weight, can be expressed as a simple determinant. For a graph with n vertices and m edges, our algorithm requires O(M(n)) elementary operations, whereM(n) is the number of elementary operations needed to multiply n n matrices. The previous best algorithm for this problem, due to Gavril [3], required O(nM(n)) operations. (Since the number of trees in a complete graph is n , our algorithm, as well as Gavril's, might involve operations on numbers of this magnitude. Such operations are accounted as elementary operations.)
منابع مشابه
Counting 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 کاملCounting and Constructing Minimal Spanning Trees
We revisit the minimal spanning tree problem in order to develop a theory of construction and counting of the minimal spanning trees in a network. The theory indicates that the construction of such trees consists of many di erent choices, all independent of each other. These results suggest a block approach to the construction of all minimal spanning trees in the network, and an algorithm to th...
متن کاملSummary of “A Distributed Algorithm for Minimum-Weight Spanning Trees”
This document summarizes the article published by Gallagerher et. al on “A Distributed Algorithm for Minimum-Weight Spanning Trees”. The asynchronous distributed algorithm determines a minimum-weight spanning tree for an undirected graph that has distinct finite weights for every edge.
متن کاملRepresenting all Minimum Spanning Trees with Applications to Counting and Generation
We show that for any edge-weighted graph G there is an equivalent graph EG such that the minimum spanning trees of G correspond one-for-one with the spanning trees of EG. The equivalent graph can be constructed in time O(m + n log n) given a single minimum spanning tree of G. As a consequence we can count the minimum spanning trees of G in time O(m+ n), generate a random minimum spanning tree i...
متن کاملLecture notes for “Analysis of Algorithms”: Minimum Spanning Trees
We present a general framework for obtaining efficient algorithms for computing minimum spanning trees. We use this framework to derive the classical algorithms of Prim, Kruskal and Bor̊uvka. We then describe the randomized linear-time algorithm of Karger, Klein and Tarjan. The algorithm of Karger, Klein and Tarjan uses deterministic linear-time implementations of a verification algorithm of Kom...
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:
- J. Algorithms
دوره 24 شماره
صفحات -
تاریخ انتشار 1997