Limits of dynamic programming

我们目前的知识动态规划的复杂性（DP复杂性）的算法问题是非常令人失望的，因为所有对最短路径问题是仅有的几个非平凡的算法问题，其DP复杂性是合理的理解。其他最短路径问题的DP复杂性以及计算机科学和生物信息学中许多基本动态规划算法的所谓最优性仍然没有得到解决。 我们遇到了同样的惨淡的情况时，近似与动态规划算法。我们的目标是制定适当的模型捕捉动态规划的范例，并证明这些模型中的重要优化问题的下界。特别是，从布尔电路复杂性和通信复杂性的强大的方法进行修改，也为动态规划算法。

Our current knowledge of the dynamic programming complexity (DP complexity) of algorithmic problems is very disappointing, since the all-pairs shortest path problem is one of only few nontrivial algorithmic problems whose DP complexity is reasonably understood. The DP complexity of other shortest path problems remains unresolved as well the alleged optimality of the many fundamental dynamic programming algorithms in computer science and bioinformatics. We encounter the same bleak situation when approximating with dynamic programming algorithms.Our goal is to formulate adequate models capturing the paradigm of dynamic programming, and to prove lower bounds for important optimization problems in these models. In particular, powerful methods from boolean circuitcomplexity and communication complexity are to be modified to work also fordynamic programming algorithms.