Low-Stretch Spanning Tree on Benchmark Circuits

We show the testing results of Kruskal, Prim-Dijkstra for finding a low-stretch spanning tree for both unweighted graphs and weighted graphs transformed from benchmark circuits [1]. On unweighted graph, our implementation can get an average stretch of about 7 for all benchmark circuits. Kruskal’s algorithm gives good edge selection for finding short stretch edges, but does not work well for other large stretch edges. Prim-Dijkstra algorithm works well on Dijkstra’s part, but not well on Prim’s part. The shortest path algorithm may not give minimum spanning tree, but it can keep the average stretch of off-tree edges very small. On random weighted graph, in which all edges are given a random weight, our implementation can get an average stretch of about 6.5 for all benchmark circuits. This result is even better than unweighted graphs. Prim-Dijkstra algorithm works better than Kruskal’s algorithm, and this is mostly due to Dijkstra’s shortest path. What’s more, a ratio for about 0.9-0.95 can make Prim-Dijkstra algorithm works even better. The low-stretch spanning tree we get is a shortest path tree, with a slightly variation to minimum spanning tree.