戒指美容问题
The ring grooming problem
摘要：
一些研究人员已经研究了支持给定流量需求所需的双向SONET环的数量最小化的问题。在这里，我们研究相关的“环疏导问题”的最小化的添加/删除位置的数量，而不是环的数量;在许多情况下，这是一个更好的近似真实的设备成本。我们的主要结果是一个新的下界的情况下，均匀交通。这使我们能够证明均匀流量的某种简单算法实际上是一种常数因子近似算法，并且它还表明一般问题的已知下界--特别是线性规划松弛--不在最佳值的常数因子内。我们还表明，我们的结果均匀的交通很容易扩展到更实际的重要情况下，准均匀的交通。最后，我们表明，如果环上的节点数是固定的，那么环疏导是在多项式时间内可解的，然而，环疏导是否是固定参数的易处理的仍然是一个悬而未决的问题。
英文摘要：
The problem of minimizing the number of bidirectional SONET rings required to support a given traffic demand has been studied by several researchers. Here we study the related ``ring grooming problem'' of minimizing the number of add/drop locations instead of the number of rings; in a number of situations this is a better approximation to the true equipment cost. Our main result is a new lower bound for the case of uniform traffic. This allows us to prove that a certain simple algorithm for uniform traffic is in fact a constant-factor approximation algorithm, and it also demonstrates that known lower bounds for the general problem--in particular, the linear programming relaxation--are not within a constant factor of the optimum. We also show that our results for uniform traffic extend readily to the more practically important case of quasi-uniform traffic. Finally, we show that if the number of nodes on the ring is fixed, then ring grooming is solvable in polynomial time; however, whether ring grooming is fixed-parameter tractable is still an open question.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
