On the set covering polytope: I. all the facets with coefficients in {0, 1, 2}
Mathematical Programming: Series A and B
A generalization of antiwebs to independence systems and their canonical facets
Mathematical Programming: Series A and B
The complexity and approximability of finding maximum feasible subsystems of linear relations
Theoretical Computer Science
SIAM Journal on Discrete Mathematics
The hardness of approximate optima in lattices, codes, and systems of linear equations
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Complexity and real computation
Complexity and real computation
Computational real algebraic geometry
Handbook of discrete and computational geometry
Diagnosing infeasibilities in network flow problems
Mathematical Programming: Series A and B
On the approximability of minimizing nonzero variables or unsatisfied relations in linear systems
Theoretical Computer Science
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We consider the problem Max FS: For a given infeasible linear system, determine a largest feasible subsystem. This problem has interesting applications in linear programming as well as in fields such as machine learning and statistical discriminant analysis. Max FS is NP-hard and also difficult to approximate. In this paper we examine structural and algorithmic properties of Max FS and of irreducible infeasible subsystems (IISs), which are intrinsically related, since one must delete at least one constraint from each IIS to attain feasibility. In particular, we establish: (i) that finding a smallest cardinality IIS is NP-hard as well as very difficult to approximate; (ii) a new simplex decomposition characterization of IISs; (iii) that for a given clutter, realizability as the IIS family for an infeasible linear system subsumes the Steinitz problem for polytopes; (iv) some results on the feasible subsystem polytope whose vertices are incidence vectors of feasible subsystems of a given infeasible system.