Maintaining Minimum Spanning Trees in Dynamic Graphs
نویسندگان
چکیده
We present the first fully dynamic algorithm for maintaining a minimum spanning tree in time o( √ n) per operation. To be precise, the algorithm uses O(n1/3 log n) amortized time per update operation. The algorithm is fairly simple and deterministic. An immediate consequence is the first fully dynamic deterministic algorithm for maintaining connectivity and, bipartiteness in amortized time O(n1/3 log n) per update, with O(1) worst case time per query.
منابع مشابه
Experimental Analysis of Algorithms for Updating Minimum Spanning Trees on Graphs Subject to Changes on Edge Weights
We consider the problem of maintaining a minimum spanning tree of a dynamically changing graph, subject to changes on edge weights. We propose an on-line fully-dynamic algorithm that runs in time O(|E|) when the easy-to-implement DRD-trees data structure for dynamic trees is used. Numerical experiments illustrate the efficiency of the approach.
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 کاملFully Sequential and Distributed Dynamic Algorithms for Minimum Spanning Trees
In this paper, we present a fully-dynamic distributed algorithm for maintaining a minimum spanning tree on general graphs with positive real edge weights. The goal of a dynamic MST algorithm is to update e ciently the minimum spanning tree after dynamic changes like edge weight changes, rather than having to recompute it from scatch each time. The rst part of the paper surveys various algorithm...
متن کاملNUMBER OF SPANNING TREES FOR DIFFERENT PRODUCT GRAPHS
In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...
متن کاملCompetitive Maintenance of Minimum Spanning Trees in Dynamic Graphs
We consider the problem of maintaining a minimum spanning tree within a graph with dynamically changing edge weights. An online algorithm is confronted with an input sequence of edge weight changes and has to choose a minimum spanning tree after each such change in the graph. The task of the algorithm is to perform as few changes in its minimum spanning tree as possible. We compare the number o...
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:
دوره شماره
صفحات -
تاریخ انتشار 1997