# Optimistic and Pessimistic Result of Planning and Scheduling Dynamie Processes

## DOI:

https://doi.org/10.7494/csci.1999.1.1.3572## Abstract

In many real-life circumstances decision problems arise. Optimisation problems can be for- mulated as decision problems as well. An optimisation problem can be expressed in terms of a model and a performance index. While the model describes the problem, the perfor mance index assigns a value to each feasible realisation of the problem [1],

An algorithm is a method to solve a class of problems with Computer. The computational complexity of an algorithm, which can be measured, is the cost. It is measured in runtime during which the algorithm is used to solve one of the problems. If the runtime is limited by a polynomial function of the amount of input data at most, the problem is said to be an easy one otherwise it is a hard problem. If a problem is easy it is enough to describe a method meeting such a constraint, when used to solve the problem. What does it mean that a problem is hard? The problem is hard when it is necessary to prove that it is impossible to find a fast method to perform the calculations which identify an optimal solution. There are a number of easy problems. Matrix inversion is easy: n * n matrix can be inverted with the Gaussian elimination method in time of cn at most. Sorting problem is easy as well. The fact that a computational problem is hard does not imply that its every instance has to be hard. The problem is hard when no algorithm can be pointed at, which could ensure a high performance for all instances of the problem. Notice that the amount of input data to the Computer in this example is smali [7].

In recent years there has been a growth in research which deals with the development and complexity analysis of combinatorial algorithms. Complexity measures are of two kinds: static, independent of the size and characteristics of the input data, and dynamie, dependent on the input data [3].

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