Constraint Satisfaction Problems over Numeric Domains

Authors Manuel Bodirsky, Marcello Mamino

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Manuel Bodirsky
Marcello Mamino

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Manuel Bodirsky and Marcello Mamino. Constraint Satisfaction Problems over Numeric Domains. In The Constraint Satisfaction Problem: Complexity and Approximability. Dagstuhl Follow-Ups, Volume 7, pp. 79-111, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


We present a survey of complexity results for constraint satisfaction problems (CSPs) over the integers, the rationals, the reals, and the complex numbers. Examples of such problems are feasibility of linear programs, integer linear programming, the max-atoms problem, Hilbert's tenth problem, and many more. Our particular focus is to identify those CSPs that can be solved in polynomial time, and to distinguish them from CSPs that are NP-hard. A very helpful tool for obtaining complexity classifications in this context is the concept of a polymorphism from universal algebra.
  • Constraint satisfaction problems
  • Numerical domains


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