the facet of knapsack ploytope, i.e. convex hull of 0-1 points satisfying a given linear inequality has been presented in this current paper. such type of facets plays an important role in set covering set partitioning, matroidal-intersection vertex- packing, generalized assignment and other combinatorial problems. strong covers for facets of knapsack ploytope has been developed in the first pa...

In the incremental knapsack problem (IK), we are given a knapsack whose capacity grows weakly as a function of time. There is a time horizon of T periods and the capacity of the knapsack is Bt in period t for t = 1, . . . , T . We are also given a set S of N items to be placed in the knapsack. Item i has a value of vi and a weight of wi that is independent of the time period. At any time period...

With growth of networked systems and applications such as ecommerce, the demand for internet security is increasing. Information can be secured using cryptography, anti-virus, malwares, spywares, firewall etc. In cryptology, cryptanalysis is a discipline where the ciphers are attacked and broke thus enabling the developers to strengthen the cipher. Nowadays cryptanalysis of ciphers is gaining p...

We observed few important facts that concerns with the new proposal of knapsack cipher 0/255, recently published by Pham [1]. The author claimed that the time complexity for solving new improved trapdoor knapsack is O(256). In this paper, we show that the knapsack cipher 0/255 can be solved in the same time that is required for solving the basic knapsack-cipher proposed by Merkle and Hellman [2...

The nonlinear Knapsack problem is to maximize a separable concave objective function, subject to a single "packing" constraint, in nonnegative variables. We consider this problem in integer and continuous variables, and also when the packing constraint is convex. Although the nonlinear Knapsack problem appears difficult in comparison with the linear Knapsack problem, we prove that its complexit...

— Recently, Hwang et al. introduced a knapsack type public-key cryptosystem. They proposed a new algorithm called permutation combination algorithm. By exploiting this algorithm, they attempt to increase the density of knapsack to avoid the low-density attack. We show that this cryptosystem is not secure, as it based on basic Merkel-Hellman knapsack cryptosystem and because of the superincreasi...

We present a highly efficient incremental algorithm for propagating bounded knapsack constraints. Our algorithm is based on the sublinear filtering algorithm for binary knapsack constraints by Katriel et al. and achieves similar speed-ups of one to two orders of magnitude when compared with its lineartime counterpart. We also show that the representation of bounded knapsacks as binary knapsacks...

We investigate a quantum dynamical entropy of one-dimesional quantum spin systems. We show that the dynamical entropy is bounded from above by a quantity which is related with group velocity determined by the interaction and mean entropy of the state. e-mail: [email protected]

A new secure knapsack cryptosystem based on the Merkle-Hellman public key cryptosystem will be proposed in this paper. Although it is common sense that when the density is low, the knapsack cryptosystem turns vulnerable to the low-density attack. The density d of a secure knapsack cryptosystem must be larger than 0 9408 . to avoid low-density attack. In this paper, we investigate a new Permutat...

The knapsack problem (KP) is generalized to the case where items are partially ordered through a set of precedence relations. As in ordinary KPs, each item is associated with profit and weight, the knapsack has a fixed capacity, and the problem is to determine the set of items to be packed in the knapsack. However, each item can be accepted only when all the preceding items have been included i...