Difference between revisions of "Open Problems:52"
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| − | We have $n$ points living in $\{1,\ldots,\Delta\}^2$ | + | We have $n$ points living in $\{1,\ldots,\Delta\}^2$. |
| − | '''Question''' | + | '''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 | Problem) of the $n$ points when streaming over the points in one pass, using | ||
| − | small space ($\log^{O(1)}\Delta$) | + | small space ($\log^{O(1)}\Delta$)? |
| − | One can achieve a $2- | + | 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 ( | + | Earth-Mover Distance over the points in the stream (see [[Open_Problems:49|Problem 49]]). |
Revision as of 04:39, 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).
