A Study of Lagrangean Decompositions and Dual Ascent Solvers for Graph Matching

TL;DR

This paper investigates Lagrangean decompositions and dual ascent algorithms for graph matching, proposing new relaxations and algorithms that improve solution quality and efficiency, especially on large-scale sparse instances.

Contribution

Introduces new Lagrangean relaxations and dual ascent algorithms for graph matching, advancing the state-of-the-art in solution quality and scalability.

Findings

New relaxations improve solution bounds.

Proposed algorithms outperform existing methods.

Effective on large-scale sparse graph instances.

Abstract

We study the quadratic assignment problem, in computer vision also known as graph matching. Two leading solvers for this problem optimize the Lagrange decomposition duals with sub-gradient and dual ascent (also known as message passing) updates. We explore s direction further and propose several additional Lagrangean relaxations of the graph matching problem along with corresponding algorithms, which are all based on a common dual ascent framework. Our extensive empirical evaluation gives several theoretical insights and suggests a new state-of-the-art any-time solver for the considered problem. Our improvement over state-of-the-art is particularly visible on a new dataset with large-scale sparse problem instances containing more than 500 graph nodes each.