Computing Partitions with Applications to the Knapsack Problem
Journal of the ACM (JACM)
A Sufficient Condition for Backtrack-Free Search
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
Toward a Model for Backtracking and Dynamic Programming
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Many hard examples in exact phase transitions
Theoretical Computer Science
Exponential Lower Bounds for the Running Time of DPLL Algorithms on Satisfiable Formulas
Journal of Automated Reasoning
The approximation power of priority algorithms
The approximation power of priority algorithms
Models of Greedy Algorithms for Graph Problems
Algorithmica
Improved exponential time lower bound of Knapsack problem under BT model
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Further reflections on a theory for basic algorithms
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
Priority algorithms for graph optimization problems
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
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We prove an @W(2^0^.^6^9^n/n) time lower bound of Knapsack problem under the adaptive priority branching trees (pBT) model. The pBT model is a formal model of algorithms covering backtracking and dynamic programming [M. Alekhnovich, A. Borodin, A. Magen, J. Buresh-Oppenheim, R. Impagliazzo, T. Pitassi, Toward a model for backtracking and dynamic programming, ECCC TR09-038, 2009. Earlier version in Proc 20th IEEE Computational Complexity, 2005, pp. 308-322]. Our result improves the @W(2^0^.^5^n/n) lower bound of M. Alekhovich et al. and the @W(2^0^.^6^6^n/n) lower bound of Li et al. [X. Li, T. Liu, H. Peng, L. Qian, H. Sun, J. Xu, K. Xu, J. Zhu, Improved exponential time lower bound of Knapsack problem under BT model, in: Proc 4th TAMC 2007, in: LNCS, vol. 4484, 2007, pp. 624-631] through optimized arguments.