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A (non-mathematician) acquaintance of mine recently proposed to me a polynomial-time algorithm for solving the traveling salesman problem. While I was able to point out a flaw in his approach, it did ...

Consider a finite set of points $V \subseteq \mathbb{R}^2 $ as a TSP-instance under the standard $\| \cdot \|_2$ norm. (TSP stands for traveling salesman tour.) We know that every optimal TSP tour $T$ ...

Define a greedy tour of a set $S=\{p_1,\ldots,p_n\}$ of $n$ points in $\mathbb{R}^2$ as produced by selecting the $i$-th point $p_i$ to start, and then connecting to the nearest neighbor $p_j$ to $p_i$...