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In the data structure field, what is the (best) term used to identify (designate) a subtree covering a subset of contiguous leaves?

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You seem to mean a subtree obtained by taking a certain node and all its successors.

In data structures, the implicit assumption usually is that we consider rooted (and often ordered) trees. Therefore, "subtree" is usually taken to mean what you intend; "subtree" as in graph-theoretic "subgraph" is rarely used (in my experience).

If you want to make very clear what you mean, you can write

The subtree of $T$ which is rooted in $x \in T$.

A common notation for this tree is $T_x$.

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  • $\begingroup$ I'm afraid you might have misunderstood the question. $\endgroup$ Commented Nov 7, 2015 at 22:08
  • $\begingroup$ @YuvalFilmus I asked in the comments (now deleted); the OP said they wanted what I state in the first paragraph. You answer follows another reasonable interpretation of the question, though. $\endgroup$
    – Raphael
    Commented Nov 7, 2015 at 23:46
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It is the subtree rooted at the least common ancestor of the set of leaves (the fact that the leaves are continuous makes no difference). I'm not sure there is any shorter term.

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