TITLE: A variation of Minkowski sum
QUESTION [7 upvotes]: I have to work with the following variation of Minkowski sum:

Let $\mathbb E$ be a Euclidean space and $K$ be a convex set in $\mathbb E\times \mathbb E$.
  Set 
  $$K^+=\{\\,x+y\in\mathbb E\mid(x,y)\in K\\,\}.$$

Note that if $K=K_x\times K_y$ for some convex sets  $K_x$ and $K_y$ in $\mathbb E$ then $K^+$ is the usual Minkowski sum of $K_x$ and $K_y$.
Questions: 

Did anyone consider this construction? 
Does it have a name?

REPLY [5 votes]: In additive combinatorics, we call the Minkowski sum the sumset, and write it as ${\mathbb E}+{\mathbb E}$. We call what you're talking about the "sumset along a graph", and write it as ${\mathbb E}+_K{\mathbb E}$, where $K$ is any graph (you call it a subset of ${\mathbb E}\times {\mathbb E}$ and I call it a graph, but it's the same thing!).
For an example of this terminology in use, check out this paper of Alon, Angel, Benjamini, and Lubetzky. Also, a google scholar search shows the terminology in action.