Linear programming with two variables per inequality in poly-log time
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Improved algorithms for linear inequalities with two variables per inequality
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Common expression analysis in database applications
SIGMOD '82 Proceedings of the 1982 ACM SIGMOD international conference on Management of data
A class of polynomially solvable range constraints for interval analysis without widenings
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2004)
Logahedra: A New Weakly Relational Domain
ATVA '09 Proceedings of the 7th International Symposium on Automated Technology for Verification and Analysis
Two variables per linear inequality as an abstract domain
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
The two variable per inequality abstract domain
Higher-Order and Symbolic Computation
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A simple algorithm is described which determines the satisfiability over the reals of a conjunction of linear inequalities, none of which contains more than two variables. In the worst case the algorithm requires time O(${mn}^{\lceil \log^2 n \rceil + 3}$), where n is the number of variables and m the number of inequalities. Several considerations suggest that the algorithm may be useful in practice: it is simple to implement, it is fast for some important special cases, and if the inequalities are satisfiable it provides valuable information about their so1ution set. The algorithm is particularly suited to applications in mechanical program verification.