Using network-flow techniques to solve an optimization problem from surface-physics

TL;DR

This paper demonstrates how network-flow algorithms, specifically the successive shortest path method, can efficiently solve a combinatorial optimization problem arising from surface physics models, notably the solid-on-solid model with defects.

Contribution

It introduces a novel application of network-flow techniques to solve a complex surface-physics optimization problem in polynomial time.

Findings

Successive shortest path algorithm solves the problem in polynomial time.

The approach effectively handles the combinatorial problem from the solid-on-solid model.

Network-flow methods can be applied to surface physics models with defects.

Abstract

The solid-on-solid model provides a commonly used framework for the description of surfaces. In the last years it has been extended in order to investigate the effect of defects in the bulk on the roughness of the surface. The determination of the ground state of this model leads to a combinatorial problem, which is reduced to an uncapacitated, convex minimum-circulation problem. We will show that the successive shortest path algorithm solves the problem in polynomial time.