We consider the following zero-sum game related to the knapsack problem. Given an instance of the knapsack problem, Alice chooses a knapsack solution and Bob chooses a cardinality k with knowing Alice’s solution. Then, Alice obtains a payoff equal to the ratio of the profit of the best k items in her solution to that of the best solution of size at most k. For α > 0, a knapsack solution is call...

We consider a variant of the knapsack problem, where items are available with different possible weights. Using a separate budget for these item improvements, the question is: Which items should be improved to which degree such that the resulting classic knapsack problem yields maximum profit? We present a detailed analysis for several cases of improvable knapsack problems, presenting constant ...

In 1978 Merkle and Hellman [11] proposed public key cryptosystems based on the knapsack problem. The simplest of these cryptosystems, the basic knapsack cryptosystem, works as follows. The public information is a set of nonnegative integers { a i : 1 ≤ i ≤ n } which are called knapsack weights. Messages are encrypted by first being broken into blocks (x 1 , ... ,x n ) of n binary digits. A bloc...

We consider maximizing a monotone submodular function under cardinality constraint or knapsack in the streaming setting. In particular, elements arrive sequentially and at any point of time, algorithm has access to only small fraction data stored primary memory. propose following algorithms taking O(ε− 1) passes: (1) (1 − e− 1 ε)-approximation for cardinality-constrained problem, (2) (0.5 knaps...

The quadratic multiple knapsack problem (QMKP) is a generalization of the quadratic knapsack problem from a single knapsack to k knapsacks. In this study, the mathematical model of the QMKP is generalized as covering the constraints that we may face in real life problems. A new hybrid algorithm which combines F-MSG algorithm and genetic algorithm is proposed to solve the Generalized QMKP (GQMKP...

We present an algorithm for the penalized multiple choice knapsack problem (PMCKP), a combination of the more common penalized knapsack problem (PKP) and multiple choice knapsack problem (MCKP). Our approach is to converts a PMCKP into a PKP using a previously known transformation between MCKP and KP, and then solve the PKP greedily. For PMCKPs with well-behaved penalty functions, our algorithm...

A necessary and sufficient condition for the identification of dominated terms in a general knapsack problem is derived. By general we mean a knapsack problem which is unbounded, equality constrained and which has a parametric right hand side. The given condition yields published results in the literature. A report on computational experiments for large scale knapsack problems, demonstrating th...

In this paper, we present a new algorithm to solve the integral knapsack problem on the hypercube. The main idea is to use the fact that the precedence graph of the dynamic programming function of the knapsack problem is an irregular mesh. We propose a scheduling algorithm for irregular meshes on the hypercube. The efficiency of the algorithm is independent on the number of processors. We also ...

The multidimensional knapsack problem is defined as an optimization problem that is NP-hard combinatorial. The multidimensional knapsack problems have large applications, which include many applicable problems from different area, like cargo loading, cutting stock, bin-packing, financial and other management, etc. This paper reviews some researches published in the literature. The concentrate i...

In this paper, we present a new class of knapsack type PKC referred to as K(III)ΣPKC. In a sharp contrast with the conventional knapsack type PKC’s, in our proposed scheme, K(I II)ΣPKC, no conventional secret sequence but the natural binary number with noise is used. We show that the coding rate, a more conservative measure for the security on knapsack PKC, can be made approximately 1.0. In App...