Improved Steiner tree approximation in graphs

The Steiner tree problem in weighted graphs seeks a minimum weight connected subgraph containing a given subset of the vertices terminals. We present a new polynomial-time heuristic with an approximation ratio approaching 1 + ln 3 2 1:55, which improves upon the previously best-known approximation algorithm of 10 with performance ratio 1:59. In quasi-bipartite graphs i.e., in graphs where all non-terminals are pairwise disjoint, our algorithm achieves an approximation ratio of 1:28, whereas the previously best method achieves an approximation ratio approaching 1:5 19 . For complete graphs with edge weights 1 and 2, we show that our heuristic has an approximation ratio approaching 1:28, which improves upon the previously best-known ratio of 4 3 4 . Our method is considerably simpler and easier to implement than previous approaches. Our techniques can also be used to prove that the Iterated 1-Steiner heuristic 14 achieves an approximation ratio of 1:5 in quasi-bipartite graphs, thus...

• Type: Conference
• Year: 2000
• Where: SODA
• Authors: Gabriel Robins, Alexander Zelikovsky
• Keywords: Algorithms, Approximation Ratio, Performance Ratio, Quasi-bipartite Graphs, SODA 2000