Watched Propagation of $$0$$-$$1$$ Integer Linear Constraints

Abstract

Efficient unit propagation for clausal constraints is a core building block of conflict-driven clause learning (CDCL) Boolean satisfiability (SAT) and lazy clause generation constraint programming (CP) solvers. Conflict-driven pseudo-Boolean (PB) solvers extend the CDCL paradigm from clausal constraints to \(0\)-\(1\) integer linear constraints, also known as (linear) PB constraints. For PB solvers, many different propagation techniques have been proposed, including a counter technique which watches all literals of a PB constraint. While CDCL solvers have moved away from counter propagation and have converged on a two watched literals scheme, PB solvers often simultaneously implement different propagation algorithms, including the counter one.