Dynamic Programming and Fast Matrix Multiplication

Abstract. We give a novel general approach for solving NP-hard optimization problems that combines dynamic programming and fast matrix multiplication. The technique is based on reducing much of the computation involved to matrix multiplication. We show that our approach works faster than the usual dynamic programming solution for any vertex subset problem on graphs of bounded branchwidth. In particular, we obtain the fastest algorithms for Planar Independent Set of runtime O(22.52 n ), for Planar Dominating Set of runtime exact O(23.99 n )

• Type: Conference
• Year: 2006
• Where: ESA
• Authors: Frederic Dorn
• Keywords: Algorithms, Dynamic Programming, ESA 2006, Fast Matrix Multiplication, Matrix Multiplication