Unbiased Statistics of a CSP - A Controlled-Bias Generator

TL;DR

This paper discusses the challenges in accurately measuring the complexity of fixed-size CSP instances and introduces a method for generating unbiased Sudoku instances, highlighting the difficulty of such tasks.

Contribution

It presents a framework for measuring CSP complexity and offers a solution for unbiased Sudoku instance generation, explaining the inherent difficulties.

Findings

Measuring CSP complexity is computationally hard.

A method for unbiased Sudoku instance generation is proposed.

The difficulty of generating unbiased instances is analyzed.

Abstract

We show that estimating the complexity (mean and distribution) of the instances of a fixed size Constraint Satisfaction Problem (CSP) can be very hard. We deal with the main two aspects of the problem: defining a measure of complexity and generating random unbiased instances. For the first problem, we rely on a general framework and a measure of complexity we presented at CISSE08. For the generation problem, we restrict our analysis to the Sudoku example and we provide a solution that also explains why it is so difficult.