Sequential Counter Encoding for Staircase At-Most-One Constraints

Hieu Xuan Truong, Tuyen Van Kieu, Khanh Van To

2025

Abstract

This paper presents a new SAT encoding to represent Staircase At-Most-One (SCAMO) constraints by combining similar sub-formulae between At-Most-One (AMO) constraints within constructing blocks. The SCAMO constraints exhibit a staircase shape due to the structural similarity between consecutive AMO constraints. The proposed method utilizes Sequential Counter (SC) encoding to represent each block in a staircase form, taking advantage of connecting the constraint representation for two consecutive blocks. Compared to the existing SCAMO representation based on Binary Decision Diagrams (BDD), our method requires fewer variables and clauses, resulting in improved solving time for SCAMO. Experimental results on real-world problems, such as Anti-bandwidth problems, demonstrate that the SC encoding representation method for SCAMO consistently outperforms alternative methods.

Paper Citation

in Harvard Style

Truong H., Van Kieu T. and Van To K. (2025). Sequential Counter Encoding for Staircase At-Most-One Constraints. In Proceedings of the 17th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART; ISBN 978-989-758-737-5, SciTePress, pages 164-175. DOI: 10.5220/0013124600003890

in Bibtex Style

@conference{icaart25,
author={Hieu Truong and Tuyen Van Kieu and Khanh Van To},
title={Sequential Counter Encoding for Staircase At-Most-One Constraints},
booktitle={Proceedings of the 17th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART},
year={2025},
pages={164-175},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013124600003890},
isbn={978-989-758-737-5},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 17th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART
TI - Sequential Counter Encoding for Staircase At-Most-One Constraints
SN - 978-989-758-737-5
AU - Truong H.
AU - Van Kieu T.
AU - Van To K.
PY - 2025
SP - 164
EP - 175
DO - 10.5220/0013124600003890
PB - SciTePress