Towards Geometry-Preserving Reductions Between Constraint Satisfaction Problems (and other problems in NP)

TL;DR

This paper introduces geometry-preserving reductions between constraint satisfaction problems and other NP-search problems, motivated by phase transitions in combinatorial optimization, providing examples and counterexamples to illustrate these reductions.

Contribution

It defines new types of reductions that preserve geometric properties, advancing understanding of problem transformations in NP.

Findings

Examples of geometry-preserving reductions

Counterexamples showing limitations of these reductions

Insights into phase transitions in combinatorial optimization

Abstract

Motivated by phase transitions in combinatorial optimization problems, we define two kinds of geometry-preserving reductions between constraint satisfaction problems and other NP-search problems. We give a couple of examples and counterexamples for these reductions.