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...

Mechanism design without money has a rich history in social choice literature. Due to thestrong impossibility theorem by Gibbard and Satterthwaite, exploring domains in which thereexist dominant strategy mechanisms is one of the central questions in the field. We propose ageneral framework, called the generalized packing problem (gpp), to study the mechanism designquestions with...

We show that there are 0-1 and unbounded knapsack polytopes with super-polynomial extension complexity. More specifically, for each n ∈ N we exhibit 0-1 and unbounded knapsack polyhedra in dimension n with extension complexity Ω(2 p n).

This paper is concerned with a variation of the multiple knapsack problem (MKP) [5, 6], where we are given a set of n items N = {1, 2, . . . , n} to be packed into m possible knapsacks M = {1, 2, . . . ,m}. As in ordinary MKP, by w j and p j we denote the weight and profit of item j ∈ N respectively, and the capacity of knapsack i ∈ M is ci. However, a fixed cost fi is imposed if we use knapsac...