Corpus ID: 224818139

A Note on the Approximability of Deepest-Descent Circuit Steps

  title={A Note on the Approximability of Deepest-Descent Circuit Steps},
  author={S. Borgwardt and Cornelius Brand and A. Feldmann and M. Kouteck{\'y}},
  • S. Borgwardt, Cornelius Brand, +1 author M. Koutecký
  • Published 2020
  • Mathematics, Computer Science
  • ArXiv
  • Linear programs (LPs) can be solved through a polynomial number of so-called deepest-descent circuit steps, each step following a circuit direction to a new feasible solution of most-improved objective function value. A computation of deepest-descent steps has recently been shown to be NP-hard [De Loera et al., arXiv, 2019]. This is a consequence of the hardness of what we call the optimal circuit-neighbor problem (OCNP) for LPs with non-unique optima. However, the non-uniqueness assumption is… CONTINUE READING


    Pivot Rules for Circuit-Augmentation Algorithms in Linear Optimization
    • 5
    • Highly Influential
    • PDF
    Evaluating and Tuning n-fold Integer Programming
    • 13
    • PDF
    NP is as easy as detecting unique solutions
    • 595
    A Polyhedral Model for Enumeration and Optimization over the Set of Circuits
    • 6
    • PDF
    A new polynomial-time algorithm for linear programming
    • 3,546
    On the foundations of linear and integer linear programming I
    • J. Graver
    • Mathematics, Computer Science
    • Math. Program.
    • 1975
    • 126
    On Augmentation Algorithms for Linear and Integer-Linear Programming: From Edmonds-Karp to Bland and Beyond
    • 18
    • PDF
    An Algorithmic Theory of Integer Programming
    • 34
    • PDF
    An implementation of steepest-descent augmentation for linear programs
    • 1
    • PDF
    On the positive sum property and the computation of Graver test sets
    • R. Hemmecke
    • Mathematics, Computer Science
    • Math. Program.
    • 2003
    • 26