近乎最佳的Manhattan型Steiner树近似算法

A Near-Optimal Approximation Algorithm for Manhattan Steiner Tree

求解最佳的 Manhattan型 Steiner树问题 (minimum rectilinear Steiner tree,简记为 MRST问题 )是在VLSI布线、网络通信中所遇到的组合优化问题 ,同时也是一个 NP-难解问题 .该文给出对该问题的 O(n2 )时间复杂性的近似算法 .该算法在最坏情况下的近似比严格小于 3/ 2 .计算机实验结果表明 ,所求得的支撑树的平均费用与最佳算法的平均费用仅相差 0 .8% .该算法稍加修改 ,可应用到三维或多维的 Manhattan空间对Steiner问题求解 ,且易于在并行与分布式环境下编程实现 .

The minimum rectilinear Steiner tree (MRST) problem is an NP complete problem which arises in VLSI wiring, network routing and many combinatorial optimization problems. In this paper, an O(n 2) time complexity approximation algorithm for MRST is proposed. The approximation ratio of the algorithm is strictly less than 3/2 . The computer verification of the algorithm shows that the costs of the produced spanning trees are only 0.8% away from the optimal. In addition, this algorithm can be revised for multidimensional Manhattan space and implemented in parallel/distributed environments easily.