Abstract
In this paper, we discuss an approach for determining the feasibility of a polyhedron defined by a system of Binary Two Variable Per Inequality (BTVPI) constraints. A constraint of the form: \(a_i\cdot x_i+a_j \cdot x_j \ge b_{ij}\) is called a BTVPI constraint, if \(a_i,a_j \in \{0,1,-1,2,-2\}\) and \(b_{ij} \in \mathbb {Z}\). These constraints find applications in a number of domains, including scheduling and abstract interpretation. Our algorithm is based on a rewrite version of the well-known Fourier-Motzkin elimination procedure for linear programs. We show that our algorithm converges in polynomial time and is faster than all known algorithms for this class of problems.
This research was made possible by the NASA Established Program to Stimulate Competitive Research, Grant # 80NSSC22M0027.
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Wojciechowski, P., Subramani, K. (2023). A Faster Algorithm for Determining the Linear Feasibility of Systems of BTVPI Constraints. In: Gąsieniec, L. (eds) SOFSEM 2023: Theory and Practice of Computer Science. SOFSEM 2023. Lecture Notes in Computer Science, vol 13878. Springer, Cham. https://doi.org/10.1007/978-3-031-23101-8_21
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