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...

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...

We model the problem of bidding in ad auctions as a penalized multiple choice knapsack problem (PMCKP), a combination of the multiple choice knapsack problem (MCKP) and the penalized knapsack problem (PKP) [1]. We present two versions of PMCKP, GlobalPMCKP and LocalPMCKP, together with a greedy algorithm that solves the linear relaxation of a GlobalPMCKP optimally. We also develop a greedy heur...