eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-08-29
12:1
12:22
10.4230/LIPIcs.CSL.2018.12
article
Submodular Functions and Valued Constraint Satisfaction Problems over Infinite Domains
Bodirsky, Manuel
1
Mamino, Marcello
2
Viola, Caterina
1
Institut für Algebra, Technische Universität Dresden, Germany
Dipartimento di Matematica, Università di Pisa, Italy
Valued constraint satisfaction problems (VCSPs) are a large class of combinatorial optimisation problems. It is desirable to classify the computational complexity of VCSPs depending on a fixed set of allowed cost functions in the input. Recently, the computational complexity of all VCSPs for finite sets of cost functions over finite domains has been classified in this sense. Many natural optimisation problems, however, cannot be formulated as VCSPs over a finite domain. We initiate the systematic investigation of infinite-domain VCSPs by studying the complexity of VCSPs for piecewise linear homogeneous cost functions. We remark that in this paper the infinite domain will always be the set of rational numbers. We show that such VCSPs can be solved in polynomial time when the cost functions are additionally submodular, and that this is indeed a maximally tractable class: adding any cost function that is not submodular leads to an NP-hard VCSP.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol119-csl2018/LIPIcs.CSL.2018.12/LIPIcs.CSL.2018.12.pdf
Valued constraint satisfaction problems
Piecewise linear functions
Submodular functions
Semilinear
Constraint satisfaction
Optimisation
Model Theory