A Note on Practical Construction of Maximum Bandwidth Paths
Jian Chen · Chinese Journal of Computers · 2001
Constructing maximum bandwidth paths has been a basic operation in the study of network routing,in particular in the recent study of network QoS routing. In the literature,it has been proposed that a maximum bandwidth path be constructed by a modified Dijkstra's algorithm or by a modified Bellman-Ford algorithm. In this short note,we present a very simple proof to show an interesting relation between a maximum spanning tree and a maximum bandwidth path. According to this proof,the Max-Bandwidth path problem can be solved based on a maximum spanning tree of the network. This observation suggests that the Max-Bandwidth path problem can be solved using Kruskal's algorithm,which is a well-known algorithm for minimum spanning tree construction. A modified Kruskal's algorithm for Max-Bandwidth path is given in this paper and compared with the modified Dijkstra's algorithm being suggested before. Although Dijkstra's algorithm and Kruskal's algorithm have the same time complexity asymptotically,Kruskal's algorithm takes a simpler form and runs much faster practically. We have programmed both algorithms and compared their performance based on a variety of network topologies. From the simulation results,we can see that for low link density networks such as mesh network,hypercube networks,networks of link density 1% and networks of link density 5%,Kruskal's algorithm in general is at least five times as fast as Dijkstra's algorithm. Even on dense networks of link density 40%,Kruskal's algorithm is still more than three times as fast as Dijkstra's algorithm. Besides the advantage of running time, we also indicate other advantages of our approach over the traditional approaches. Our results should have significant impact on the research and implementation of network applications.