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Dynamic Programming (DP) is a fundamental problem-solving technique that has been widely used for solving a broad range of search and optimization problems. While DP can be invoked when more specialized methods fail, this generality often incurs a cost in ef?ciency. We explore a toolkit for speeding up DP, and algorithms that use DP as subroutines. The toolkit includes: - Acceleration via Compression - Totally Monotone Matrice - Combining Compression and Total Monotonicity - Partial Tables - Fractional Subproblems