Editing Open Problems:23
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.
| Latest revision | Your text | ||
| Line 1: | Line 1: | ||
| − | {{ | + | {{DISPLAYTITLE:Problem 23: Approximate 2D Width}} |
| − | | | + | {{Infobox |
| − | | | + | |label1 = Proposed by |
| + | |data1 = Pankaj Agarwal and Piotr Indyk | ||
| + | |label2 = Source | ||
| + | |data2 = [[Workshops:Kanpur_2009|Kanpur 2009]] | ||
| + | |label3 = Short link | ||
| + | |data3 = http://sublinear.info/23 | ||
}} | }} | ||
The width of a set $P$ of points in the plane is defined as | The width of a set $P$ of points in the plane is defined as | ||
| − | \[ \ | + | \[ \mbox{width}(P)=\min_{\|a\|_2=1} \left(\max_{p \in P} a \cdot p-\min_{p \in P} a |
\cdot p\right). \] | \cdot p\right). \] | ||
For a stream of insertions and deletions of points from a $[\Delta] \times [\Delta]$ grid, we would like to maintain an approximate width of the point set. We conjecture that there is an algorithm for this problem that achieves a constant approximation factor and uses $\operatorname{polylog}(\Delta+n)$ space. | For a stream of insertions and deletions of points from a $[\Delta] \times [\Delta]$ grid, we would like to maintain an approximate width of the point set. We conjecture that there is an algorithm for this problem that achieves a constant approximation factor and uses $\operatorname{polylog}(\Delta+n)$ space. | ||
