For the following, $(w,x) >= (y,z)$ iff $w >= y$ and $x >= z$.I have a list, $L$, of $k$ points with integer coordinates ranging from $0$ to $n-1$.  Each point has an associated set.  I would like a data structure that can perform the following:$include(x,y,i)$ - include the element $i$ to all of the sets associated with a point $p$, where $p >= (x,y)$$remove(x,y,i)$ - remove the element $i$ from all of the sets associated with a point $p$, where $p >= (x,y)$$retrieve(x,y)$ - retrieve the set associated with point $p = (x,y)$My intuition is telling me that $include$ and $remove$ should be possible in something like $\text{polylog}(k)$ and $retrieve$ should be possible in something like $\text{polylog}(k) \times (\text{size of set})$.  The 2-dimensional aspect of this is stumping me, however.Motivation: this data structure could be very useful for quickly calculating edit distances for a data set I'm using at work.
2-dimensional dynamic set retrieval
ds.algorithms;ds.data structures;dynamic algorithms