Finite-resolution hidden surface removal
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Point containment in the integer hull of a polyhedron
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Splitting the Control Flow with Boolean Flags
SAS '08 Proceedings of the 15th international symposium on Static Analysis
Certainty closure: Reliable constraint reasoning with incomplete or erroneous data
ACM Transactions on Computational Logic (TOCL)
Approximating a real number by a rational number with a limited denominator: A geometric approach
Discrete Applied Mathematics
Two variables per linear inequality as an abstract domain
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
An efficient and quasi linear worst-case time algorithm for digital plane recognition
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Reducing the coefficients of a two-dimensional integer linear constraint
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Efficient lattice width computation in arbitrary dimension
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Computing efficiently the lattice width in any dimension
Theoretical Computer Science
The two variable per inequality abstract domain
Higher-Order and Symbolic Computation
The exact lattice width of planar sets and minimal arithmetical thickness
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Widening polyhedra with landmarks
APLAS'06 Proceedings of the 4th Asian conference on Programming Languages and Systems
A polynomial algorithm for one problem of guillotine cutting
Operations Research Letters
On the linear ranking problem for integer linear-constraint loops
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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An optimal algorithm is presented for computing the smallest set of linear inequalities that define the integer hull of a possibly unbounded two-dimensional convex polygon R. Input to the algorithm is a set of linear inequalities defining R, and the integer hull computed is the convex hull of the integer points of R. It is proven that the integer hull has at most O(n log Amax) inequalities, where n is the number of input inequalities and Amax is the magnitude of the largest input coefficient. It is shown that the algorithm presented has complexity O(n log Amax) and that this is optimal by proving that the integer hull may have $\Omega(n \log A_{max})$ inequalities in the worst case.