We construct three public key knapsack cryptosystems. Standard knapsack cryptosystems hide easy instances of the knapsack problem and have been broken. The systems considered in the article face this problem: They hide a random (possibly hard) instance of the knapsack problem. We provide both complexity results (size of the key, time needed to encypher/decypher...) and experimental results. Sec...

In the last lecture, we studied the KNAPSACK problem. The KNAPSACK problem is an NP-hard problem but does admit a pseudo-polynomial time algorithm and can be solved efficiently if the input size is small. We used this pseudo-polynomial time algorithm to obtain an FPTAS for KNAPSACK. In this lecture, we study another class of problems, known as strongly NP-hard problems. Definition 1 (Strongly N...

Finding approximate solutions to hard combinatorial optimization problems by neu-ral networks is a very attractive prospect. Many empirical studies have been done in the area. However, recent research about a neural network model indicates that for any NP-hard problem the existance of a polynomial size network that solves it implies that NP=co-NP, which is contrary to the well-known conjecture ...

Assigning facilities to locations is one of the important problems, which significantly is influence in transportation cost reduction. In this study, we solve quadratic assignment problem (QAP), using a meta-heuristic algorithm with deterministic tasks and equality in facilities and location number. It should be noted that any facility must be assign to only one location. In this paper, first o...

Instance complexity was introduced by Orponen, Ko, Schh oning, and Watanabe 14] as a measure of the complexity of individual instances of a decision problem. Comparing instance complexity to Kolmogorov complexity, they introduced the notion of p-hard instances, and conjectured that every set not in P has p-hard instances. Whereas this conjecture is still unsettled, Fortnow and Kummer 6] proved ...