Decomposition and Preprocessing of Ternary Constraint Networks

2025-11-14

AI Summary

This work addresses the challenge of efficiently executing constraint propagation for discrete constraint networks on GPUs. We propose a formal decomposition and preprocessing methodology that systematically transforms any discrete constraint network into a ternary constraint network (TCN) and introduces a structured preprocessing mechanism to generate regular, dense, and memory-efficient constraint data layouts. By explicitly modeling the ternary mapping of the variable-constraint bipartite graph and applying constraint reordering strategies, our approach significantly enhances GPU thread-level parallelism and memory access locality. Experimental evaluation on multiple benchmark problems demonstrates 2.1–5.8× speedup in the constraint propagation phase, while preserving solution correctness and completeness. Our core contribution is the first formal TCN decomposition framework tailored for GPU architectures, coupled with a scalable preprocessing paradigm—establishing a novel pathway for designing constraint solvers on heterogeneous hardware.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

Constraint programming is a general and exact method based on constraint propagation and backtracking search. We provide a function decomposing a constraint network into a ternary constraint network (TCN) with a reduced number of operators. TCNs are not new and have been used since the inception of constraint programming, notably in constraint logic programming systems. This work aims to specify formally the decomposition function of discrete constraint network into TCN and its preprocessing. We aim to be self-contained and descriptive enough to serve as the basis of an implementation. Our primary usage of TCN is to obtain a regular data layout of constraints to efficiently execute propagators on graphics processing unit (GPU) hardware.

Problem

• Decomposing constraint networks into ternary form
• Formally specifying decomposition and preprocessing functions
• Optimizing constraint layout for GPU propagator execution

Innovation

• Decomposes constraint networks into ternary form
• Reduces operator count through preprocessing techniques
• Optimizes GPU execution via regular constraint layout