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M.Aleknovich et al. have recently proposed a model of algorithms, called BT model, which generalizes both the priority model of Borodin, Nielson and Rackoff, as well as a simple dynamic programming model by Woeginger. BT model can be further divided into three kinds of fixed, adaptive and fully adaptive ones. They have proved exponential time lower bounds of exact and approximation algorithms under adaptive BT model for Knapsack problem. Their exact lower bound is $Omega(2^{0.5n}/sqrt{n})$, in this paper, we slightly improve the exact lower bound to about $Omega(2^{0.69n}/sqrt{n})$, by the same technique, with related parameters optimized.
MapReduce (and its open source implementation Hadoop) has become the de facto platform for processing large data sets. MapReduce offers a streamlined computational framework by interleaving sequential and parallel computation while hiding underlying
We prove that with high probability over the choice of a random graph $G$ from the ErdH{o}s-Renyi distribution $G(n,1/2)$, a natural $n^{O(varepsilon^2 log n)}$-time, degree $O(varepsilon^2 log n)$ sum-of-squares semidefinite program cannot refute th
Francis Castro, et al [2] computed the exact divisibility of families of exponential sums associated to binomials $F(X) = aX^{d_1} + bX^{d_2}$ over $mathbb{F}_p$, and a conjecture is presented for related work. Here we study this question.
The problem of distinguishing between a random function and a random permutation on a domain of size $N$ is important in theoretical cryptography, where the security of many primitives depend on the problems hardness. We study the quantum query compl
We prove that with high probability over the choice of a random graph $G$ from the ErdH{o}s-Renyi distribution $G(n,1/2)$, the $n^{O(d)}$-time degree $d$ Sum-of-Squares semidefinite programming relaxation for the clique problem will give a value of a