Matrices of Optimal Tree-Depth and Row-Invariant Parameterized Algorithm for Integer Programming

  title={Matrices of Optimal Tree-Depth and Row-Invariant Parameterized Algorithm for Integer Programming},
  author={Timothy F. N. Chan and Jacob W. Cooper and Martin Kouteck{\'y} and Daniel Kr{\'a}l and Krist{\'y}na Pek{\'a}rkov{\'a}},
A long line of research on fixed parameter tractability of integer programming culminated with showing that integer programs with n variables and a constraint matrix with tree-depth d and largest entry Δ are solvable in time g(d,Δ) poly(n) for some function g, i.e., fixed parameter tractable when parameterized by tree-depth d and Δ. However, the tree-depth of a constraint matrix depends on the positions of its non-zero entries and thus does not reflect its geometric structure. In particular… 
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