Generalized Totalizer Encoding for Pseudo-Boolean Constraints
This incremental improvement addresses efficiency in SAT solving for real-world optimization problems modeled with pseudo-Boolean constraints.
The paper tackles the problem of encoding pseudo-Boolean constraints into SAT formulas by proposing Generalized Totalizer Encoding (GTE), which reduces auxiliary variable dependency to the number of distinct coefficient combinations rather than their magnitudes, showing superiority for constraints with few distinct coefficients and remaining competitive otherwise.
Pseudo-Boolean constraints, also known as 0-1 Integer Linear Constraints, are used to model many real-world problems. A common approach to solve these constraints is to encode them into a SAT formula. The runtime of the SAT solver on such formula is sensitive to the manner in which the given pseudo-Boolean constraints are encoded. In this paper, we propose generalized Totalizer encoding (GTE), which is an arc-consistency preserving extension of the Totalizer encoding to pseudo-Boolean constraints. Unlike some other encodings, the number of auxiliary variables required for GTE does not depend on the magnitudes of the coefficients. Instead, it depends on the number of distinct combinations of these coefficients. We show the superiority of GTE with respect to other encodings when large pseudo-Boolean constraints have low number of distinct coefficients. Our experimental results also show that GTE remains competitive even when the pseudo-Boolean constraints do not have this characteristic.