Expected computation time for Hamiltonian path problem
SIAM Journal on Computing
Dynamic Programming Treatment of the Travelling Salesman Problem
Journal of the ACM (JACM)
Computing Partitions with Applications to the Knapsack Problem
Journal of the ACM (JACM)
Introduction to Algorithms
Algorithms
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Fourier meets möbius: fast subset convolution
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Dynamic Programming for Minimum Steiner Trees
Theory of Computing Systems
Set Partitioning via Inclusion-Exclusion
SIAM Journal on Computing
Exact parameterized multilinear monomial counting via k-layer subset convolution and k-disjoint
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Counting perfect matchings as fast as Ryser
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Planar k-path in subexponential time and polynomial space
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Reducing a target interval to a few exact queries
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Homomorphic hashing for sparse coefficient extraction
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Fast monotone summation over disjoint sets
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Finding small separators in linear time via treewidth reduction
ACM Transactions on Algorithms (TALG)
Space---Time tradeoffs for subset sum: an improved worst case algorithm
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Exponential approximation schemata for some network design problems
Journal of Discrete Algorithms
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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. Our approach is based on algebraic methods and turns out to be useful for several other problems as well. Then we show how the framework yields polynomial space exact algorithms for the classical Traveling Salesman, Weighted Set Cover and Weighted Steiner Tree problems as well. Our algorithms match the time bound of the best known pseudo-polynomial space algorithms for these problems.