this article addresses a multi-stage flowshop scheduling problem with equal number of unrelated parallel machines. the objective is to minimize the makespan for a given set of jobs in the system. this problem class is np-hard in the strong sense, so a hybrid heuristic method for sequencing and then allocating operations of jobs to machines is developed. a number of test problems are randomly ge...

The main aim of NP-completeness theory is the analysis of intractabil-ity. Many optimization problems were rst proved to be NP-hard. Since the complete solution of these problems requires exponential time, polynomial time algorithms to nd \near-optimal" solutions, i.e., approximation algorithms, appear to be viable. In this paper we show the basic principles of Approximation Theory for NP-compl...

Though integer factorization and discrete logarithm problem are both practically and theoretically important, the computational complexity of these problems remained unknown. By comparing integer factorization problem with a problem in P and NP-complete problems, I show that the decision problem version of integer factorization problem is neither in P nor NP-complete. In addition, integer facto...

Ehrenfeucht-Fraı̈ssé games and their generalizations have been quite successful in finite model theory and yield various inexpressibility results. However, for key problems such as P 6= NP or NP 6= co-NP no progress has been achieved using the games. We show that for these problems it is already hard to get the board for the corresponding Ehrenfeucht-Fraı̈ssé game. We obtain similar results for t...

the recent years have witnessed an increasing attention to the methods of multiple attribute decision making in solving the problems of the real world due to their shorter time of calculation and easy application. one of these methods is the ‘permutation method’ which has a strong logic in connection with ranking issues, but when the number of alternatives increases, solving problems through th...

Deadlocks are very serious system failures and have been observed in existing packet switching networks (PSN's). Several problems related to the design of deadlock-free PSN's are investigated here. Polynomial-time algorithms are given for some of these problems, but most of them are shown to be NP-complete or NP-hard, and therefore polynomial-time algorithms are not likely to be found.