Source coding by efficient selection of ground states clusters

TL;DR

This paper extends Survey Propagation to handle external forces, enabling efficient exploration of complex solution spaces in NP-complete problems and introduces a novel lossy data compression method leveraging clustered ground states.

Contribution

It generalizes Survey Propagation for external forcing, demonstrating efficient solution space exploration and proposing a new compression protocol based on clustered states.

Findings

Evidence of replica symmetry breaking in large instances

Efficient exploration of exponential solution spaces

Introduction of a new lossy compression method

Abstract

In this letter, we show how the Survey Propagation algorithm can be generalized to include external forcing messages, and used to address selectively an exponential number of glassy ground states. These capabilities can be used to explore efficiently the space of solutions of random NP-complete constraint satisfaction problems, providing a direct experimental evidence of replica symmetry breaking in large-size instances. Finally, a new lossy data compression protocol is introduced, exploiting as a computational resource the clustered nature of the space of addressable states.