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Transition Dominance in Domain-Independent Dynamic Programming

Authors J. Christopher Beck , Ryo Kuroiwa , Jimmy H. M. Lee , Peter J. Stuckey , Allen Z. Zhong

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial optimization
Keywords
  • Dominance
  • Dynamic Programming
  • Combinatorial Optimization

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Abstract

Domain-independent dynamic programming (DIDP) is a model-based paradigm for dynamic programming (DP) that enables users to define DP models based on a state transition system. Heuristic search-based solvers have demonstrated strong performance in solving combinatorial optimization problems. In this paper, we formally define transition dominance in DIDP, where one transition consistently leads to better solutions than another, allowing the search process to safely ignore dominated transitions. To facilitate the efficient use of transition dominance, we introduce an interface for defining transition dominance and propose the use of state functions to cache values, thereby avoiding redundant computations when verifying transition dominance. Experimental results on DP models across multiple problem classes indicate that incorporating transition dominance and state functions yields a 5 to 10 times speed-up on average for different search algorithms within the DIDP framework compared to the baseline.

Cite As Get BibTex

J. Christopher Beck, Ryo Kuroiwa, Jimmy H. M. Lee, Peter J. Stuckey, and Allen Z. Zhong. Transition Dominance in Domain-Independent Dynamic Programming. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CP.2025.5

Author Details

J. Christopher Beck
  • Department of Mechanical and Industrial Engineering, University of Toronto, Canada
Ryo Kuroiwa
  • National Institute of Informatics, Tokyo, Japan
  • The Graduate School of Advanced Studies, SOKENDAI, Tokyo, Japan
Jimmy H. M. Lee
  • Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong
Peter J. Stuckey
  • Department of Data Science and AI, Monash University, Clayton, Australia
  • ARC Training Centre OPTIMA, Melbourne, Australia
Allen Z. Zhong
  • Department of Data Science and AI, Monash University, Clayton, Australia
  • ARC Training Centre OPTIMA, Melbourne, Australia

Funding

This work was supported by the Australian Research Council OPTIMA ITTC IC200100009, a General Research Fund (CUHK14206321) by the Hong Kong University Grants Committee, a Direct Grant by CUHK, and the Natural Sciences and Engineering Research Council of Canada.

Supplementary Materials

References

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