# Problem 52: TSP in the Streaming Model

From Open Problems in Sublinear Algorithms

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).