Editing Open Problems:52
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: | ||
{{Header | {{Header | ||
+ | |title=TSP in the streaming model | ||
|source=dortmund12 | |source=dortmund12 | ||
|who=Christian Sohler | |who=Christian Sohler | ||
}} | }} | ||
− | We have $n$ points living in $\{1,\ldots,\Delta\}^2$. | + | We have $n$ points living in $\{1,\ldots,\Delta\}^2$ space. |
− | '''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 (has appeared previously as [[Open_Problems:49|Problem 49]]). |