# Generalized Totalizer Encoding for Pseudo-Boolean Constraints

arXiv: https://arxiv.org/abs/1507.05920 · HTML: https://mlsanity.com/paper/1507.05920/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2015.

## Built on by (most cited first, 6 of 6)

- [SAT Encodings for Pseudo-Boolean Constraints Together With At-Most-One Constraints](https://mlsanity.com/paper/2110.08068/) (2021)
- [Learning to Select SAT Encodings for Pseudo-Boolean and Linear Integer Constraints](https://mlsanity.com/paper/2307.09342/) (2023)
- [Certifying Pareto-Optimality in Multi-Objective Maximum Satisfiability](https://mlsanity.com/paper/2501.17493/) (2025)
- [New Core-Guided and Hitting Set Algorithms for Multi-Objective Combinatorial Optimization](https://mlsanity.com/paper/2204.10856/) (2022)
- [ParLS-PBO: A Parallel Local Search Solver for Pseudo Boolean Optimization](https://mlsanity.com/paper/2407.21729/) (2024)
- [Exact and approximate determination of the Pareto set using minimal correction subsets](https://mlsanity.com/paper/2204.06908/) (2022)

## Abstract (arXiv)

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.