计算直线最小斯坦纳树的最佳算法是什么?
有许多算法可以找到直线 Steiner 最小树 (RSMT) 的近似值。其中包括:
- 一套寻找最小生成树的算法
- RST-T(直线单主干 Steiner 树)
- BGA(批量贪婪算法)
- BI1S(批量迭代 1-Steiner 树)
- FLUTE(基于快速查找表的 RSMT 构造和线长技术)估计)
表明RSMT的长度可以达到直线生成最小树长度的3/2。我在文献中没有找到其他算法的范围。它们存在吗?
FLUTE 似乎是最有效的算法,但我不知道它的最坏情况和上限。被发现了吗?
有没有任何算法的界限小于 3/2?
There are many algorithms that find approximations of rectilinear Steiner minimum trees (RSMT). Among them are:
- a suite of algorithms that find minimum spanning trees
- RST-T (rectilinear single trunk Steiner tree)
- BGA (batcheed greedy algorithm)
- BI1S (Batched Iterated 1-Steiner tree)
- FLUTE (Fast Lookup Table Based Technique for RSMT Construction and Wirelength Estimation)
It was showed that length of RSMT can be as much as 3/2 times that of rectlinear spanning minimum tree. I didn't find in literature bounds for other algorithms. Do they exist?
FLUTE seems to be the most efficient algorithm from all but I don't know it's worst case and upper bound. Was it found?
Does any algorithm have bound less than 3/2?
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阿罗拉 和 Mitchell 给出了多项式时间近似方案(= 对于所有 epsilon > 0,欧几里得施泰纳树的 (1 + epsilon)-近似值。我相信这些想法可以直接适应直线变体。
Arora and Mitchell gave polynomial-time approximation schemes (= for all epsilon > 0, a (1 + epsilon)-approximation) for Euclidean Steiner tree. I believe the ideas can be adapted straightforwardly to the rectilinear variant.