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Download Chemical Process Structures and Information Flows by Richard S.H. Mah, Howard Brenner, Andreas Acrivos and James PDF

By Richard S.H. Mah, Howard Brenner, Andreas Acrivos and James E. Bailey (Auth.)

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Each step in an algorithm must be capable of an unique and unambiguous interpretation, and also as a matter of practicality, it must be implementable, at least in principle. The notion of definiteness also applies to the outcome of its execution. For any properly prescribed input of a problem instance, the algorithm must produce a definite output or solution. The second attribute of an algorithm is its finiteness. It cannot go on ad infinitum. It must terminate after a finite number of steps, and preferably, after a small number of steps.

The notion of definiteness also applies to the outcome of its execution. For any properly prescribed input of a problem instance, the algorithm must produce a definite output or solution. The second attribute of an algorithm is its finiteness. It cannot go on ad infinitum. It must terminate after a finite number of steps, and preferably, after a small number of steps. Chap. 2 Graphs and Digraphs 55 The third attribute of an algorithm is that it must be efficient. In a broad sense, the notion of efficiency relates the utilization of a resource to accomplish a task among alternatives.

1 1 1! 1 Fig. 2-28 A fundamental circuit matrix. In an analogous manner we can define a fundamental cutset matrix, Κ whose rows correspond to the fundamental cutsets (with respect to a given spanning tree) and whose columns correspond to the edges of a connected digraph. The sign of each nonzero entry is determined by comparison with the direction corresponding to the branch which determines the cutset. This (N - 1) by 5 matrix can be so arranged that the branches corresponding to each fundamental cutset appear in that order before the chords.

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