3 research outputs found
A separator theorem for hypergraphs and a CSP-SAT algorithm
We show that for every r≥2 there exists ϵr>0 such that any r-uniform hypergraph with m edges and maximum vertex degree o(m−−√) contains a set of at most (12−ϵr)m edges the removal of which breaks the hypergraph into connected components with at most m/2 edges. We use this to give an algorithm running in time d(1−ϵr)m that decides satisfiability of m-variable (d,k)-CSPs in which every variable appears in at most r constraints, where ϵr depends only on r and k∈o(m−−√). Furthermore our algorithm solves the corresponding #CSP-SAT and Max-CSP-SAT of these CSPs. We also show that CNF representations of unsatisfiable (2,k)-CSPs with variable frequency r can be refuted in tree-like resolution in size 2(1−ϵr)m. Furthermore for Tseitin formulas on graphs with degree at most k (which are (2,k)-CSPs) we give a deterministic algorithm finding such a refutation
A Separator Theorem for Hypergraphs and a CSP-SAT Algorithm
We show that for every there exists such that any
-uniform hypergraph with edges and maximum vertex degree
contains a set of at most edges the removal of
which breaks the hypergraph into connected components with at most edges.
We use this to give an algorithm running in time that
decides satisfiability of -variable -CSPs in which every variable
appears in at most constraints, where depends only on and
. Furthermore our algorithm solves the corresponding #CSP-SAT
and Max-CSP-SAT of these CSPs. We also show that CNF representations of
unsatisfiable -CSPs with variable frequency can be refuted in
tree-like resolution in size . Furthermore for Tseitin
formulas on graphs with degree at most (which are -CSPs) we give a
deterministic algorithm finding such a refutation