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I'm learning vantage point trees, and I met this while reading the paper Data Structures and Algorithms for Nearest Neighbor Search in General Metric Spaces by Peter Yianilos (Proceedings of SODA 1993, SIAM, pages 311–321; PDF). The following pseudocode appears in Algorithm 1.

$$\begin{align*} \hspace{2em}&\hspace{-2em} \textbf{function}\text{ Make_vp_tree(}S\text{)}\\ &\textbf{if }S=\emptyset\textbf{ then return }\emptyset\\ &\text{new(node);}\\ &\text{node}\!\uparrow\!\!\text{.p} := \text{Select_vp(}S\text{);}\\ &\text{node}\!\uparrow\!\!\text{.mu} := \text{Median}_{s\in S}\, d(p,s);\\ &\dotsc \end{align*}$$

node is a node of vp-tree, so I know what node.p means, but what do that up arrow means in this context?

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The algorithms in the paper you link to are described in a notation quite similar to Pascal, a language that treats pointers in a very particular way. In Pascal, pointers are declared as references to values of specific types (a pointer to an integer can never refer to a boolean, for instance).

The upward arrow, in the example you reproduce, is a dereferencing operator. Clearly, node is a pointer to a value of a record type (not a record itself), of which p and mu are fields, so node.p has no meaning.

Check out this similar question for further clarification.

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