Trees and hills: methodology for maximizing functions of systems of linear relations
Trees and hills: methodology for maximizing functions of systems of linear relations
The complexity and approximability of finding maximum feasible subsystems of linear relations
Theoretical Computer Science
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
Fast Heuristics for the Maximum Feasible Subsystem Problem
INFORMS Journal on Computing
A two-phase relaxation-based heuristic for the maximum feasible subsystem problem
Computers and Operations Research
Branch-and-Cut for the Maximum Feasible Subsystem Problem
SIAM Journal on Optimization
On the approximability of the maximum feasible subsystem problem with 0/1-coefficients
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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It is a folklore result that testing whether a given system of equations with two variables per inequality (a 2VPI system) of the form xi−xj=cij is solvable, can be done efficiently not only by Gaussian elimination but also by shortest-path computation on an associated constraint graph. However, when the system is infeasible and one wishes to delete a minimum weight set of inequalities to obtain feasibility (MinFs2=), this task becomes NP-complete. Our main result is a 2-approximation for the problem MinFs2= for the case when the constraint graph is planar using a primal-dual approach. We also give an α-approximation for the related maximization problem MaxFs2= where the goal is to maximize the weight of feasible inequalities. Here, α denotes the arboricity of the constraint graph. Our results extend to obtain constant factor approximations for the case when the domains of the variables are further restricted.