Improved Exponential Time Lower Bound of Knapsack Problem Under BT Model

On exponential time lower bound of Knapsack under backtracking

“…However, it turns out that this is not an easy task. So far the only successful effort is that Li et al have improved the lower bound of Knapsack under adaptive pBT model to Ω(2 0.66n / √ n) [17].…”

“…Then in a subsequent work [17], the authors set β = 2/3 − and γ = 1/3 − , still keeping a ratio β/γ = 2, which leads to…”

“…An interesting and natural question from the seminal work on pBT model of Alekhovich et al [1] appears as what is the best possible lower bound of Knapsack under pBT model [17]? In other words, can we show tight bound of Knapsack under pBT model?…”

“…Recently we can see a stream of works concerning formal definitions of models of commonly used algorithms such as greedy and dynamic programming and showing (exponential) lower bounds of (N P -hard) interesting computational problems, mainly conducted by Allan Borodin and Russell Impagliazzo with their students and collaborators [7,4,8,1,5,10,3,6,17,21,12,11]. This line of research is interesting and important, since for these N P -hard problems we still cannot prove any exponential time lower bound under very general algorithmic models without proving that P = N P (thus settling a major scientific open problem), it is reasonable to formally define some restricted algorithmic models and to characterize their powers with lower bounds of computational problems.…”