Supnick matrix
Monge Array, Symmetric Matrix, Main Diagonal, Distance Matrix, Travelling Salesman Problem, NP-hard
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A Supnick matrix or Supnick array named after Fred Supnick of the City College of New York, who introduced the notion in 1957 is a Monge array which is also a symmetric matrix.A Supnick matrix is a square Monge array that is symmetric around the main diagonal.An n-by-n matrix is a Supnick matrix if, for all i, j, k, l such that if 1\le i k\le n and 1\le j l\le n then a_{ij} + a_{kl} \le a_{il} + a_{kj}\, and also a_{ij} = a_{ji}. \, A logically equivalent definition i...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A Supnick matrix or Supnick array named after Fred Supnick of the City College of New York, who introduced the notion in 1957 is a Monge array which is also a symmetric matrix.A Supnick matrix is a square Monge array that is symmetric around the main diagonal.An n-by-n matrix is a Supnick matrix if, for all i, j, k, l such that if 1\le i k\le n and 1\le j l\le n then a_{ij} + a_{kl} \le a_{il} + a_{kj}\, and also a_{ij} = a_{ji}. \, A logically equivalent definition is given by Rudolf & Woeginger who in 1995 proved that A matrix is a Supnick matrix iff it can be written as the sum of a sum matrix S and a non-negative linear combination of LL-UR block matrices.
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