We investigate how efficiently a well-studied family of domination-type problems can be
solved on bounded-treewidth graphs. For sets σ, ρ of non-negative integers, a (σ, ρ)-set of a
graph G is a set S of vertices such that| N (u)∩ S|∈ σ for every u∈ S, and| N (v)∩ S|∈ ρ for
every v∉ S. The problem of finding a (σ, ρ)-set (of a certain size) unifies standard problems
such as INDEPENDENT SET, DOMINATING SET, INDEPENDENT DOMINATING SET, and
many others. For all pairs of finite or cofinite sets (σ, ρ), we determine (under standard …

We investigate how efficiently a well-studied family of domination-type problems can be
solved on bounded-treewidth graphs. For sets $\sigma,\rho $ of non-negative integers, a
$(\sigma,\rho) $-set of a graph $ G $ is a set $ S $ of vertices such that $| N (u)\cap
S|\in\sigma $ for every $ u\in S $, and $| N (v)\cap S|\in\rho $ for every $ v\not\in S $. The
problem of finding a $(\sigma,\rho) $-set (of a certain size) unifies standard problems such
as Independent Set, Dominating Set, Independent Dominating Set, and many others. For all …