Accelerating dynamic programming

[摘要] (cont.) In the heart of this method are algorithms for computing the edit distance between two straight-line programs. These enable us to exploits the compressibility of strings, even if each string is compressed using a different compression scheme. - Partial Tables. In typical DP settings, a table is filled in its entirety, where each cell corresponds to some subproblem. In some cases, by changing the DP, it is possible to compute asymptotically less cells of the table. We show that [theta](n³) subproblems are both necessary and sufficient for computing the similarity between two trees. This improves all known solutions and brings the idea of partial tables to its full extent. - Fractional Subproblems. In some DPs, the solution to a subproblem is a data structure rather than a single value. The entire data structure of a subproblem is then processed and used to construct the data structure of larger subproblems. We suggest a method for reusing parts of a subproblem;;s data structure. In some cases, such fractional parts remain unchanged when constructing the data structure of larger subproblems. In these cases, it is possible to copy this part of the data structure to the larger subproblem using only a constant number of pointer changes. We show how this idea can be used for finding the optimal tree searching strategy in linear time. This is a generalization of the well known binary search technique from arrays to trees.

[发布机构] Massachusetts Institute of Technology