On Planar Valued CSPs

We study the computational complexity of planar valued constraint satisfaction problems (VCSPs). First, we show that intractable Boolean VCSPs have to be self-complementary to be tractable in the planar setting, thus extending a corresponding result of Dvořák and Kupec [ICALP’15] from CSPs to VCSPs. Second, we give a complete complexity classification of conservative planar VCSPs on arbitrary finite domains. As it turns out, in this case planarity does not lead to any new tractable cases, and thus our classification is a sharpening of the classification of conservative VCSPs by Kolmogorov and Živný [JACM’13]. 1998 ACM Subject Classification F.2 Analysis of Algorithms and Problem Complexity