The paper presents new criteria for bijectivity/transitivity of Tfunctions and fast knapsack-like algorithm of evaluation of a T-function. Our approach is based on non-Archimedean ergodic theory: Both the criteria and algorithm use van der Put series to represent 1-Lipschitz p-adic functions and to study measure-preservation/ergodicity of these.

A new approach for identifying a friend aircrafts from foe (IFF) using public-key cryptosystem is introduced. Two schemes of public-key cryptosystem namely: RSA and knapsack public-keys are considered, which provide higher security than conventional identification methods. The practical aspects of using such systems for aircraft identification purposes are discussed. Computer simulation example...

A new approach for identifying a friend aircrafts from foe (IFF) using public-key cryptosystem is introduced. Two schemes of public-key cryptosystem namely: RSA and knapsack public-keys are considered, which provide higher security than conventional identification methods. The practical aspects of using such systems for aircraft identification purposes are discussed. Computer simulation example...

We consider the 0–1 Knapsack Problem with Setups. We propose an exact approach which handles the structure of the ILP formulation of the problem. It relies on partitioning the variables set into two levels and exploiting this partitioning. The proposed approach favorably compares to the algorithms in literature and to solver CPLEX 12.5 applied to the ILP formulation. It turns out to be very eff...

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...

The stochastic non-linear fractional knapsack problem is a challenging optimization problem with numerous applications, including resource allocation. The goal is to find the most valuable mix of materials that fits within a knapsack of fixed capacity. When the value functions of the involved materials are fully known and differentiable, the most valuable mixture can be found by direct applicat...

where the pairs (I+$, Xi) 2 0 are assumed to be independent draws from a common . . . . . joint distribution Fwx. If we think of the pairs (w,Xi) as the weights and values, respectively, of a collection of n objects, then this problem can be thought of as finding the collection of objects of maximum value which will fit in a “knapsack” with weight capacity 1. Our main result, Theorem 2.4, compu...

Motivated by a real world application, we study the multiple knapsack problem with assignment restrictions (MKAR): We are given a set of items N = f1; : : : ; ng and a set of knapsacks M = f1; : : : ;mg. Each item j 2 N has a positive real weight wj and each knapsack i 2 M has a positive real capacity ci associated with it. In addition, for each item j 2 N a set Aj M of knapsacks that can hold ...

In this paper, we present a new methodology to adapt any kind of lattice reduction algorithms to deal with the modular knapsack problem. In general, the modular knapsack problem can be solved using a lattice reduction algorithm, when its density is low. The complexity of lattice reduction algorithms to solve those problems is upper-bounded in the function of the lattice dimension and the maximu...

A new approach for identifying a friend aircrafts from foe (IFF) using public-key cryptosystem is introduced. Two schemes of public-key cryptosystem namely: RSA and knapsack public-keys are considered, which provide higher security than conventional identification methods. The practical aspects of using such systems for aircraft identification purposes are discussed. Computer simulation example...