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.
@article{arxiv.1612.05476,
title = {A Study of Lagrangean Decompositions and Dual Ascent Solvers for Graph Matching},
author = {Paul Swoboda and Carsten Rother and Hassan Abu Alhaija and Dagmar Kainmueller and Bogdan Savchynskyy},
journal= {arXiv preprint arXiv:1612.05476},
year = {2017}
}