Modelling Langford's Problem: A Viewpoint for Search

TL;DR

This paper compares various models for solving Langford's Problem, demonstrating that a channelled model with static branching order performs best, and highlighting the effectiveness of different base models for propagation and search order.

Contribution

It introduces and empirically evaluates multiple models derived from two viewpoints, identifying the most effective approach for solving Langford's Problem.

Findings

Channelled model with static branching order outperforms others

One base model excels in propagation efficiency

Another base model provides an effective static search order

Abstract

The performance of enumerating all solutions to an instance of Langford's Problem is sensitive to the model and the search strategy. In this paper we compare the performance of a large variety of models, all derived from two base viewpoints. We empirically show that a channelled model with a static branching order on one of the viewpoints offers the best performance out of all the options we consider. Surprisingly, one of the base models proves very effective for propagation, while the other provides an effective means of stating a static search order.