Height and Depth in a DAG

Mon, 01 Jan 0001 00:00:00 +0000

A recurring question when working with dependency DAGs is what to call this quantity:

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level(v) = 0                                  if v has no dependencies
         = 1 + max(level(d) for d in deps(v)) otherwise

A node with nothing below it is 0; every other node is one more than the deepest thing it depends on. Is that height or depth? The short answer: by the standard tree analogy it is height, but the word is convention-dependent and the only safe practice is to define the recurrence explicitly rather than rely on the label. This page explains why the ambiguity exists and how to reason about it precisely.

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Height and Depth in a DAG