Contested Cluster Selectors: Local Ambiguity, Normal Forms, and Backtracking Cost in Random Constraint Satisfaction (opens in new tab)

We introduce and empirically investigate \emph{contested cluster selectors} (\CCS): variables that are non-backbone, carry information about solution-cluster identity, and are repeatedly but unreliably forced by local propagation during backtracking search. In instrumented \DPLL{} experiments on random 3-\SAT{} near the empirical satisfiability threshold and on near-optimal random \VC{} instances, a small number of such variables accounts for a ...