---
title: "Compact Modeling in Constraint Programming with Hybrid Tables"
authors:
  - "Christophe Lecoutre"
  - "Mouny Samy Modeliar"
  - "Gilles Audemard"
  - "Nicolas Paris"
  - "Nicolas Szczepanski"
doi: "10.24963/ijcai.2026/255"
url: "https://ijcai.org/proceedings/2026/255"
pdf: "https://ijcai.org/proceedings/2026/0255.pdf"
venue: "Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence"
year: 2026
pages: "2291-2299"
track: "Main Track"
keywords:
  - "Constraint Satisfaction and Optimization: Modeling"
  - "Constraint Satisfaction and Optimization: Constraint optimization problems"
  - "Constraint Satisfaction and Optimization: Constraint satisfaction"
  - "Constraint Satisfaction and Optimization: Constraint programming"
---

# Compact Modeling in Constraint Programming with Hybrid Tables

Christophe Lecoutre, Mouny Samy Modeliar, Gilles Audemard, Nicolas Paris, Nicolas Szczepanski

*Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence*, pages 2291-2299. DOI: [10.24963/ijcai.2026/255](https://doi.org/10.24963/ijcai.2026/255)

## Abstract

Hybrid tables, also referred to  as `smart' in the literature, represent a valuable modeling technique within Constraint Programming (CP). These tables allow us to handle disjunctive cases (constraining expressions) in a compact and structured way, by authorizing tuples (table entries) to contain simple unary and binary arithmetic restrictions (similar to internal constraints).
In this paper, we show the practical interest of using hybrid tables for planning-like combinatorial puzzles, when the transition from one state to the next can be encoded by a single hybrid table. 
Experimental results show that these hybrid models exhibit greater compactness and efficiency in solving compared to their conventional counterparts.