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.