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“Computer programs usually operate on tables of information. In most cases these tables are not simply amorphous masses of numerical values, they involve important structural relationship between the data elements.”

Knuth, Art of Computer Programming, vol. 1 (Fundamental algorithms), 3rd edition, p. 252.

My question is what does “structural relationship between the elements” mean. How are these structures different from any mathematical structure?

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    $\begingroup$ Knuth might be referring to databases. There is a lot of information out there on databases. $\endgroup$ – Yuval Filmus May 9 '20 at 9:00
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    $\begingroup$ Another option is that Knuth is referring to data structures in general. Again, there is a lot of information out there. $\endgroup$ – Yuval Filmus May 9 '20 at 9:00
  • $\begingroup$ What does structural relationship means is not discussed. Classification of structural relationships is also not discussed by Knuth. So what does structural relationship means and what is the classification of that types of structures and how these structures are different from discrete structures is my basic question. $\endgroup$ – Rakesh Kumar Katare May 9 '20 at 11:45
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    $\begingroup$ You are treating Knuth as scripture. He's just making a very general comment. It doesn't have any specific meaning. It seems to be confusing you. I suggest ignoring it, and focusing on the technical content of Knuth's tome. $\endgroup$ – Yuval Filmus May 9 '20 at 11:46
  • $\begingroup$ How relationships is structural $\endgroup$ – Rakesh Kumar Katare May 9 '20 at 11:49
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Your citation is incorrect--this is on page 232 in 3rd edition, not 252 (first paragraph of "Information Structures", chapter 2.1.

Based on having the chapter available, Knuth is talking about data structures in general. I agree the with suggestions above--just ignore this paragraph if it doesn't make sense or seems obvious. I personally agree that it does not seem to define anything or communicate anything clear to me.

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Structural relationship between data items deals directly with the architecture of machine under which we are exploring structural relationships so we can say that structural relationship is based on the architecture of machine. If it is a parallel architecture then we have parallel data structures ,if it is a sequential architecture then we have sequential data structures , but here we have mathematical models under which we can explain above types of data structures so we say that we are dealing with a class of structures which is based on architectural structures for exploring structural relationships between the data items.

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