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Augmenting the Cumulative Overload Check with Integral Resource Usage Reasoning

Authors Samuel Cloutier , Claude-Guy Quimper

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LIPIcs.CP.2026.13.pdf
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Subject Classification

ACM Subject Classification
  • Computing methodologies → Planning and scheduling
  • Theory of computation → Constraint and logic programming
Keywords
  • Scheduling
  • Cumulative constraint
  • Knapsacks
  • Overload check

Metrics

Abstract

Few amongst the rules that filter the Cumulative constraint reason on the integrity of resource consumption. We augment the overload check with an integral reasoning that better evaluates resource availability. This reasoning is based on the knapsack problem, which we solve using dynamic programming. Our new rule subsumes the time table horizontally elastic overload check while its running time complexity is 𝒪(C n²), only increasing by a factor C (the resource capacity) due to solving knapsack problems. Exploiting word-parallelism actually makes this complexity 𝒪(C/w n²) for w-bit machines. On usual instances, C is small and this complexity collapses back to 𝒪(n²). Our algorithm generates explanations for lazy clause generation solvers. With our new knapsack augmented overload check, we are able to solve all but 5 instances of the Pack benchmark. By performing a small transformation of the instances, we show that our method is more robust than known pre-solving methods that perform well on the original benchmark.

Cite As Get BibTex

Samuel Cloutier and Claude-Guy Quimper. Augmenting the Cumulative Overload Check with Integral Resource Usage Reasoning. In 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 379, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.CP.2026.13

Author Details

Samuel Cloutier
  • Université Laval, Québec, Canada
Claude-Guy Quimper
  • Université Laval, Québec, Canada

Supplementary Materials

References

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