Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
Randomized online scheduling on two uniform machines
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Exact arithmetic at low cost—a case study in linear programming
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
The reliable algorithmic software challenge RASC
Computer Science in Perspective
A near-optimal strategy for a heads-up no-limit Texas Hold'em poker tournament
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
Fast and Accurate Bounds on Linear Programs
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
On Using Floating-Point Computations to Help an Exact Linear Arithmetic Decision Procedure
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
The reliable algorithmic software challenge RASC
WEA'03 Proceedings of the 2nd international conference on Experimental and efficient algorithms
Solving Very Sparse Rational Systems of Equations
ACM Transactions on Mathematical Software (TOMS)
An exact rational mixed-integer programming solver
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Integration of an LP solver into interval constraint propagation
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Exact solutions to linear programming problems
Operations Research Letters
Computer Science Review
Operations Research Letters
Improving the accuracy of linear programming solvers with iterative refinement
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Valid Linear Programming Bounds for Exact Mixed-Integer Programming
INFORMS Journal on Computing
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State-of-the-art linear programming (LP) solvers give solutions without any warranty. Solutions are not guaranteed to be optimal or even close to optimal. Of course, it is generally believed that the solvers produce optimal or at least close to optimal solutions.We have implemented a system LPex which allows us to check this belief. More precisely, given an LP and a basis B, it determines whether the basis is primal feasible and/or dual feasible. It can also find the optimum starting from an arbitrary basis (or from scratch). It uses exact arithmetic to guarantee correctness of the results. The system is efficient enough to be applied to medium- to large-scale LPs. We present results from the netlib benchmark suite.