Phase Transition in the Number Partitioning Problem

TL;DR

This paper uses statistical mechanics to analyze the number partitioning problem, revealing a phase transition that distinguishes easy instances from hard ones, and provides insights into its computational complexity.

Contribution

It introduces a phase transition analysis for number partitioning, connecting computational difficulty with statistical mechanics concepts.

Findings

Identifies a phase transition separating easy and hard instances.

Calculates the phase diagram and typical ground state energy.

Links the problem's complexity to pseudo-polynomiality.

Abstract

Number partitioning is an NP-complete problem of combinatorial optimization. A statistical mechanics analysis reveals the existence of a phase transition that separates the easy from the hard to solve instances and that reflects the pseudo-polynomiality of number partitioning. The phase diagram and the value of the typical ground state energy are calculated.