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@ARTICLE{Capelli:859646,
      author       = {Capelli, Riccardo and Caracciolo, Sergio and Di Gioacchino,
                      Andrea and Malatesta, Enrico M.},
      title        = {{E}xact value for the average optimal cost of the bipartite
                      traveling salesman and two-factor problems in two
                      dimensions},
      journal      = {Physical review / E},
      volume       = {98},
      number       = {3},
      issn         = {2470-0045},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2019-00494},
      pages        = {030101},
      year         = {2018},
      abstract     = {We show that the average optimal cost for the
                      traveling-salesman problem in two dimensions, which is the
                      archetypal problem in combinatorial optimization, in the
                      bipartite case, is simply related to the average optimal
                      cost of the assignment problem with the same Euclidean,
                      increasing, convex weights. In this way we extend a result
                      already known in one dimension where exact solutions are
                      avalaible. The recently determined average optimal cost for
                      the assignment when the cost function is the square of the
                      distance between the points provides therefore an exact
                      $prediction\overline{E_{N}}$ = $\frac{1}{\pi}$ $\log$ Nfor
                      large number of points 2N. As a byproduct of our analysis
                      also the loop covering problem has the same optimal average
                      cost. We also explain why this result cannot be extended at
                      higher dimensions. We numerically check the exact
                      predictions.},
      cin          = {IAS-5},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IAS-5-20120330},
      pnm          = {899 - ohne Topic (POF3-899)},
      pid          = {G:(DE-HGF)POF3-899},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000445970500001},
      doi          = {10.1103/PhysRevE.98.030101},
      url          = {https://juser.fz-juelich.de/record/859646},
}