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My questions is: What is the "real" difference between Reverse nearest neighbor(RNN) and Nearest neighbor(NN) queries? In my opinion, these two should return same result.

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The definition given by

Papadias D., Tao Y. (2009) Reverse Nearest Neighbor Query. In: LIU L., ÖZSU M.T. (eds) Encyclopedia of Database Systems. Springer, Boston, MA

states that

Given a multi-dimensional dataset $P$ and a point $q$, a reverse nearest neighbor (RNN) query retrieves all the points $p\in{P}$ that have $q$ as their nearest neighbor.

As a simple example, consider the 1D point set $P=[a,b,c]=[0,2,3]$. Then we have \begin{align} \mathrm{NN}(a) &= b \\ \mathrm{NN}(b) &= c \\ \mathrm{NN}(c) &= b \end{align} So \begin{align} \mathrm{RNN}(a) &= \emptyset \\ \mathrm{RNN}(b) &= \{a,c\} \\ \mathrm{RNN}(c) &= b \end{align} Does this help?

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  • $\begingroup$ I got the logic, Exactly what i was looking for simple yet informative. Thank you! $\endgroup$
    – user331172
    May 29 '17 at 4:21
  • $\begingroup$ @GeoMatt22 The reverse nearest neighbour relation is not a symmetric relation. $\endgroup$
    – Dylan
    May 29 '19 at 13:34
  • $\begingroup$ Could you include a full reference in case the link goes dead in the future? $\endgroup$ Jun 7 '20 at 11:09
  • $\begingroup$ @RichardHardy done. $\endgroup$
    – GeoMatt22
    Jun 8 '20 at 2:28

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