Saving space by algebraization
Daniel Lokshtanov, Jesper Nederlof · 2010
The Subset Sum and Knapsack problems are fundamental NP-complete problems and the pseudo-polynomial time dynamic programming algorithms for them appear in every algorithms textbook. The algorithms require pseudo-polynomial time and space. Since we do not expect polynomial time algorithms for Subset Sum and Knapsack to exist, a very natural question is whether they can be solved in pseudo-polynomial time and polynomial space. In this paper we answer this question affirmatively, and give the first pseudo-polynomial time, polynomial space algorithms for these problems.