Question

Discuss the principal operations involve in designing non deterministic algorithms

Answer 1

The influence of Richard Bellman is seen in algorithms throughout the computer science literature. Bellman’s principle of optimality has been used to develop highly efficient dynamic programming solutions to many important and difficult problems. The paradigm is now well entrenched as one of the most successful algorithm design tools employed by computer scientists. The optimality principle was given a broad and general statement by Bellman [23, making it applicable to problems of diverse types. Since computer programs are often employed to implement solutions based on the principle of optimality, Bellman’s impact on computing in general has been immense. In this paper we wish to focus in particular on the influence of Bellman’s work on the area of computer science known as algorithm design and analysis. A primary goal of algorithm design and analysis is to discover theoretical properties of classes of algorithms (e.g., how efficient they are, when they are applicable) and thus learn how to better apply the algorithms to new problems. From the perspective of algorithm design and analysis, combinatorial optimization problems form the class of problems on which the principle of optimality has had its greatest impact. Problem decomposition is a basic technique for attacking problems of this type-the solution to a large problem is obtained by combining solutions to smaller subproblems. The trick of this approach, of course, is to define an efficient decomposition procedure which assures that combining optimal solutions to subproblems will result in an optimal solution to the larger problem. As a standard course of action, computer scientists attempt to define a decomposition 97 0022-247X/86 $3.00 Copyngh, , 1986 by Academrc Press. Inc All n&his 01 reproductton m any form re%vcd 98 PAULHELMAN based on Bellman’s principle of optimality. Problem decompositions based on the principle of optimality not only are at the heart of dynamic programming algorithms, but are also integral parts of the strategies of other important classes of algorithms, such as branch and bound. The remainder of this paper is divided into three sections. Each section attempts to illustrate the manner in which Bellman’s principle of optimality has influenced researchers addressing issues arising in one particular area of algorithm design and analysis. Section 2 samples several problems with important applications directly in computer science. These problems have been successfully solved by algorithms based on the principle of optimality. Section 3 considers the class of NP-complete problems-a large class of problems for which it is strongly believed that no efficient (i.e., subexponential time) algorithms exist. We discuss how, for some of these problems, the principle of optimality has been used to construct algorithms which are acceptable in certain situations. The final section discusses how the principle of optimality has been incorporated as a key component of several formal models of optimization algorithms. We summarize some significant theoretical results obtained from these models concerning the applicability and efficiency of dynamic programming.  

Answer 2

Answer:

In computer science, a nondeterministic algorithm is an algorithm that, even for the same input, can exhibit different behaviors on different runs, as opposed to a deterministic algorithm. There are several ways an algorithm may behave differently from run to run.