Difference between revisions of "Open Problems:52"
| Line 12: | Line 12: | ||
One can achieve a $2$-approximation by computing a minimum spanning tree | One can achieve a $2$-approximation by computing a minimum spanning tree | ||
in small space, and use the MST to approximate TSP. The question is | in small space, and use the MST to approximate TSP. The question is | ||
| − | whether one can obtain an approximation factor $c < 2$ in polylog space | + | whether one can obtain an approximation factor $c < 2$ in polylog space. |
| − | |||
There are other natural related question, such as computing the | There are other natural related question, such as computing the | ||
Earth-Mover Distance over the points in the stream (see [[Open_Problems:49|Problem 49]]). | Earth-Mover Distance over the points in the stream (see [[Open_Problems:49|Problem 49]]). | ||
Revision as of 04:40, 12 December 2012
| Suggested by | Christian Sohler |
|---|---|
| Source | Dortmund 2012 |
| Short link | https://sublinear.info/52 |
We have $n$ points living in $\{1,\ldots,\Delta\}^2$.
Question: Can we approximate the value of the TSP tour (Traveling Salesman Problem) of the $n$ points when streaming over the points in one pass, using small space ($\log^{O(1)}\Delta$)?
One can achieve a $2$-approximation by computing a minimum spanning tree in small space, and use the MST to approximate TSP. The question is whether one can obtain an approximation factor $c < 2$ in polylog space. There are other natural related question, such as computing the Earth-Mover Distance over the points in the stream (see Problem 49).
