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3_dimensional_matching_numerical (857B)

      1 # Numerical 3DM
      2 
      3 https://en.wikipedia.org/wiki/Numerical_3-dimensional_matching
      4 
      5 NUMERICAL 3-DIMENSIONAL MATCHING: [vertices] are integers and the [edges] are
      6 all triples that sum to the same value S/n where S is the sum of all the X Y Z
      7 
      8 [np_complete] by reduction from [3-PARTITION] following
      9 http://courses.csail.mit.edu/6.892/spring19/scribe/lec2.pdf simply by adding
     10 large values
     11 
     12 still [strongly_NP_hard] even when two of the three sets are {1,2,...,n}, see [yu2004minimizing]
     13 
     14 still [strongly_NP_hard] even when all 3n input integers are required to be pairwise distinct
     15 - cf [hulett2008multigraph] Corollary 8
     16 - generalized to [ASP_hardness] in [mit2024tetris] Theorem 3
     17 
     18 See also: [3_dimensional_matching], [3_partition]
     19 
     20 Up: [computational_problem]
     21 
     22 Aliases: numerical 3DM, N3DM, numerical 3-dimensional matching, numerical 3 dimensional matching