LIPIcs.CP.2024.37.pdf
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Computing Small Rainbow Cycle Numbers with SAT Modulo Symmetries (Short Paper)
Authors
Markus Kirchweger 
,
Stefan Szeider
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30th International Conference on Principles and Practice of Constraint Programming (CP 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Principles and Practice of Constraint Programming (CP) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-08-29
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Markus Kirchweger and Stefan Szeider. Computing Small Rainbow Cycle Numbers with SAT Modulo Symmetries (Short Paper). In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 37:1-37:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CP.2024.37
https://doi.org/10.4230/LIPIcs.CP.2024.37
Abstract
Envy-freeness up to any good (EFX) is a key concept in Computational Social Choice for the fair division of indivisible goods, where no agent envies another’s allocation after removing any single item. A deeper understanding of EFX allocations is facilitated by exploring the rainbow cycle number (R_f(d)), the largest number of independent sets in a certain class of directed graphs. Upper bounds on R_f(d) provide guarantees to the feasibility of EFX allocations (Chaudhury et al., EC 2021).
In this work, we precisely compute the numbers R_f(d) for small values of d, employing the SAT modulo Symmetries framework (Kirchweger and Szeider, CP 2021). SAT modulo Symmetries is tailored specifically for the constraint-based isomorph-free generation of combinatorial structures. We provide an efficient encoding for the rainbow cycle number, comparing eager and lazy approaches. To cope with the huge search space, we extend the encoding with invariant pruning, a new method that significantly speeds up computation.
Subject Classification
ACM Subject Classification
- Mathematics of computing → Extremal graph theory
- Software and its engineering → Constraint and logic languages
- Hardware → Theorem proving and SAT solving
- Mathematics of computing → Graph enumeration
Keywords
- EFX
- rainbow cycle number
- SAT modulo Symmetries
- combinatorial search
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References
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