On exponential time lower bound of Knapsack under backtracking

Abstract

Keywords:Model of algorithms The pBT model Knapsack problem Exponential time lower bounds Backtracking a b s t r a c t We prove an Ω(2 0.69n / √ 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 Ω(2 0.5n / √ n) lower bound of M. Alekhovich et al. and the Ω(2 0.66n / √ n) lower bound of Li et al. , 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.