Paper Info
Title
Semidefinite programming approach for the quadratic assignment problem with a sparse graph.
Abstract
The matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in practice, but such SDPs typically scale badly, involving matrix variables of dimension where is the number of nodes. To achieve a speed up, we propose a further relaxation of the SDP involving a number of positive semidefinite matrices of dimension no greater than the number of edges in one of the graphs. The relaxation can be further strengthened by considering cliques in the graph, instead of edges. The dual problem of this novel relaxation has a natural three-block structure that can be solved via a convergent Alternating Direction Method of Multipliers in a distributed manner, where the most expensive step per iteration is computing the eigendecomposition of matrices of dimension . The new SDP relaxation produces strong bounds on quadratic assignment problems where one of the graphs is sparse with reduced computational complexity and running times, and can be used in the context of nuclear magnetic resonance spectroscopy to tackle the assignment problem.
Year
DOI
Venue
2018
https://doi.org/10.1007/s10589-017-9968-8
Comp. Opt. and Appl.
Keywords
Field
DocType
Graph matching,Quadratic assignment problem,Convex relaxation,Semidefinite programming,Alternating direction method of multipliers
Adjacency matrix,Discrete mathematics,Combinatorics,Mathematical optimization,Quadratic assignment problem,Positive-definite matrix,Matching (graph theory),Assignment problem,Mathematics,Semidefinite programming,Computational complexity theory,Dense graph
Journal
Volume
Issue
ISSN
69
3
0926-6003
Citations 
PageRank 
References 
1
0.35
19
Authors
3
Name
Order
Citations
PageRank
José F. S. Bravo Ferreira110.35
Yuehaw Khoo2326.04
A. Singer369552.77