This paper presents and analyzes cryptanalytic attacks on knapsack public key cryptosystems that are based on ideas from Diophantine approximation. Shamir’s attack on the basic Merkle-Hellman knapsack cryptosystem is shown to depend on the existence of ‘‘unusually good’’ simultaneous Diophantine approximations to a vector constructed from the public key. This aspect of Shamir’s attack carries o...

& is called a knapsack constraint. The special case of the MKP01 with %*!) is the classical knapsack problem (KP01), whose usual statement is the following. Given a knapsack of capacity and objects, each being associated a profit (gain) and a volume occupation, one wants to select + ( +, and + not fixed) objects such that the total profit is maximized and the capacity of the knapsack is not exc...

In the analysis of complex stochastic dynamic programs (DPs), we often seek strong theoretical guarantees on the suboptimality of heuristic policies: a common technique for obtaining such guarantees is perfect information analysis. This approach provides bounds on the performance of an optimal policy by considering a decision maker who has access to the outcomes of all future uncertainties befo...

In this paper, we study the online unweighted knapsack problem with removal cost. The input is a sequence of items u1, u2, . . . , un, each of which has a size and a value, where the value of each item is assumed to be equal to the size. Given the ith item ui, we either put ui into the knapsack or reject it with no cost. When ui is put into the knapsack, some items in the knapsack are removed w...

During the last decades, much research has been conducted on deriving classes of valid inequalities for mixed integer knapsack sets, which we call knapsack cuts. Bixby et al. (The sharpest cut: the impact of Manfred Padberg and his work. MPS/SIAM Series on Optimization, pp. 309–326, 2004) empirically observe that, within the context of branch-and-cut algorithms to solve mixed integer programmin...

0/1 Multiple Knapsack Problem, a generalization of more popular 0/1 Knapsack Problem, is NP-hard and considered harder than simple Knapsack Problem. 0/1 Multiple Knapsack Problem has many applications in disciplines related to computer science and operations research. Quantum Inspired Evolutionary Algorithms (QIEAs), a subclass of Evolutionary algorithms, are considered effective to solve diffi...

The size of the Pareto curve for the bicriteria version of the knapsack problem is polynomial on average. This has been shown for various random input distributions. We experimentally investigate the number of Pareto optimal knapsack fillings. Our experiments suggests that the theoretically proven upper bound of O(n3) for uniform instances and O(φμn4) for general probability distributions is no...

Abstract Ensemble-based methods are highly popular approaches that increase the accuracy of a decision by aggregating opinions individual voters. The common point is to maximize accuracy; however, natural limitation occurs if incremental costs also assigned Consequently, we investigate creating ensembles under an additional constraint on total cost members. This task can be formulated as knapsa...