Problem 52: TSP in the Streaming Model

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Suggested by Christian Sohler
Source Dortmund 2012
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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).