Editing Travelling salesman problem (section)

====Upper bound====
*One has <math>L^*\le 2\sqrt{n}+2</math>, and therefore <math>\beta\leq 2</math>, by using a naïve path which visits monotonically the points inside each of <math>\sqrt n</math> slices of width <math>1/\sqrt{n}</math> in the square.
*Few<ref>{{cite journal|last1=Few|first1=L.|title=The shortest path and the shortest road through n points|journal=[[Mathematika]]|date=1955|volume=2|issue=2|pages=141–144|doi=10.1112/s0025579300000784 }}</ref> proved <math>L^*_n\le\sqrt{2n}+1.75</math>, hence <math>\beta\le\sqrt 2</math>, later improved by Karloff (1987): <math>\beta\le0.984\sqrt2</math>.
* Fietcher<ref>{{cite journal|last1=Fiechter|first1=C.-N.|title=A parallel tabu search algorithm for large traveling salesman problems|journal=Disc. Applied Math.|date=1994|volume=51|issue=3|pages=243–267 |doi=10.1016/0166-218X(92)00033-I|doi-access=free}}</ref> empirically suggested an upper bound of <math>\beta\le 0.73\dots</math>.