eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2024-08-29
35:1
35:9
10.4230/LIPIcs.CP.2024.35
article
On the Complexity of Integer Programming with Fixed-Coefficient Scaling (Short Paper)
de Vlas, Jorke M.
1
Linköping Universitet, Sweden
We give a polynomial time algorithm that solves a CSP over 𝐙 with linear inequalities of the form c^{a₁} x - c^{a₂} y ≤ b where x and y are variables, a₁, a₂ and b are parameters, and c is a fixed constant. This is a step in classifying the complexity of CSP(Γ) for first-order reducts Γ from (𝐙, < ,+,1). The algorithm works by first reducing the infinite domain to a finite domain by inferring an upper bound on the size of the smallest solution, then repeatedly merging consecutive constraints into new constraints, and finally solving the problem using arc consistency.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol307-cp2024/LIPIcs.CP.2024.35/LIPIcs.CP.2024.35.pdf
constraint satisfaction problems
integer programming
CSP dichotomy