eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-12-01
4:1
4:14
10.4230/LIPIcs.MFCS.2017.4
article
The Complexity of Boolean Surjective General-Valued CSPs
Fulla, Peter
Zivny, Stanislav
Valued constraint satisfaction problems (VCSPs) are discrete optimisation problems with the objective function given as a sum of fixed-arity functions; the values are rational numbers or infinity.
In Boolean surjective VCSPs variables take on labels from D={0,1} and an optimal assignment is required to use both labels from D. A classic example is the global min-cut problem in graphs. Building on the work of Uppman, we establish a dichotomy theorem and thus give a complete complexity classification of Boolean surjective VCSPs. The newly discovered tractable case has an interesting structure related to projections of downsets and upsets. Our work generalises the dichotomy for {0,infinity}-valued constraint languages corresponding to CSPs) obtained by Creignou and Hebrard, and the dichotomy for {0,1}-valued constraint languages (corresponding to Min-CSPs) obtained by Uppman.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol083-mfcs2017/LIPIcs.MFCS.2017.4/LIPIcs.MFCS.2017.4.pdf
constraint satisfaction problems
surjective CSP
valued CSP
min-cut
polymorphisms
multimorphisms